I have a 10ee in somewhat distant storage, where I can't easily check it, so this topic is near and dear. I think it's a pretty complicated subject. A lot depends on the storage environment, how often and when the doors will be opened, etc. Apologies for the length.. Other perspectives appreciated.
Peanut butter holding dry dog kibble works.
I am not a fan of bait in traps anywhere around machines or in storage areas. It can attract the very beasts you are trying to avoid. If you bait it, they will come. I prefer to leave them unbaited, in key traffic areas. Poison baits can also attract, sometimes very much so. Some are stronger baits than others. One thing worse than the smell of mouse piss is the smell of rotting mice.
Is there anything that should be done to protect the electricals, and open frame motors? I know some electrical cleaners include protective coatings but I'm not sure what does more harm than good. Desiccant in the main cabinet is a no-brainer. Round dial owners will have exposed end-gears in the main cabinet. What about pulley rust? For longer term storage, removing belts and lubing those related surfaces may be a consideration.
You might install a lamp inside the cabinet. If not for maintaining temps while in storage, then for warming the machine before unwrapping. Leaving lamps of any wattage powered in a machine while unattended makes me nervous. I suppose there are ways to do it safely, and there are products made specifically for that purpose. In checking machine temps in spring with an IR pyrometer, I find it can take them months to warm up. Having the lamp(s) already installed allows you to warm a machine before unwrapping it, even if only to check it and touch up protective coatings.
I recently learned about Brooding lamps, for keeping chicks warm. They are available from farm supply stores, like TSC. They are typically high quality ceramic sockets, reflectors, and cages to prevent bulb contact. I paid $7 each this past spring for nice US made units. They sell IR bulbs for the brooding application but those tend to be too powerful for anything but brief internal use - 250 watts. You might choose a bulb sized for continuous use in storage, possibly rigged to a timer. You could put it in the lower center cabinet, if you have room, or under the bed. With a 10ee, there's plenty of room in the head end.
They sell 100% silica gel for use as cat litter. It's a good source for locally available bulk SG (it seems to be universally available at walmart, not so available elsewhere). I'm sure it works fine as-is for cat piss but I prefer to gently bake it for a few hours at 250F or so to make sure it is fully dry before using it in a critical application. You can make your own packets of it, in any size.
Paste wax can be difficult to apply, especially to uneven surfaces or to parts of an EE that aren't perfectly clean. I find it can be difficult to tell if a surface is completely covered with paste wax. Waxes for machine protection often have dyes so you can see coverage. It's hard to wax around the bed rollers, on the ways under the saddle, etc. It is critical to seal the seams and crevices. If condensation occurs, and we must assume it will, it will tend to wick into seams, where it will be trapped and cause unseen corrosion. Wax can also have issues with formation of pin holes or cracks that may not be obvious but leave surfaces unprotected. How does the wax interface with way oil, and oil in seams? Does that create areas of incomplete coverage? There is going to be way oil under the saddle, cross slide, etc - at least I hope.
I see a lot of Monarch's with pitting on their serial number plate and pitting on round dials. Don't forget to protect those well. The crank dials and knurls also rust.
Plenty of people like fluid film, others lps 3. Plenty of folks with huge amounts of experience protecting machines in storage express a preference for LPS 3. Plenty of threads on the topic. FF is highly regarded and quite different from other products. I have a can of FF here but haven't found the time to test it. I've used LPS 3 quite a bit, and their tech support for tech questions is very good. The pump sprayer is more reliable than the aerosol (don't spray the aerosol when it is cold!), though the aerosol atomizes better. You might order a gallon of it, Zoro and Travers had the best prices, last I checked. Often applying it with a brush is best. The company currently specs the shelf life at 10 years but I'm told only because their parent company forced them to set a time limit. Previously it was 'indefinite', so no worries about that. It's better if you don't allow any of these products to freeze.
Fwiw, the application temp - ambient and machine temp - can be big factors in how effective those products are and how they behave during and after application. When applied in the cold or to cold machinery, it's hard for the solvent to evaporate. You want it to firm up and resist being wiped off by a cover, etc. With LPS 3, and many others, the best application method seems to be a thin coat so it gets a good firm skin as a base. And then apply a second coat, a day or two later. If you spray it on thick, a surface barrier forms that traps the carrier solvent. That keeps it from firming up anytime soon, and maybe for a long while.
Some of the better products are designed to recover protection even after a scratch is put in the coating. Like if the machine cover wipes across it.
The instructions of one inexpensive product I tried suggests "putting it on thick!" I followed their directions and it was a big mistake and a big waste. It foamed on the surface, due to the rapid escape of the propellant (when you spray a lot of it, the can cools and the propellant comes out in the coating). It remained a soft mush weeks after application, potentially with voids, that was easily wiped off. This really pissed me off, because I drove downstate during a window in the weather to protect some machines. I had to return to do it over. I contacted the mfg, and it was obvious they never tested their own product or directions. After some prodding, they decided to test their product and decided thick was bad. They are revising the label, they told me. They didn't even offer to replace the product I wasted. I don't want to give them any PR by naming them. It's basically a spray vaseline.
And then there are various mil-spec products, some heavy wax based. For some applications I like a brush on product. It's important to seal the seams and interfaces of the machine well, because those crevices tend to wick moisture. It's also important that the surface be very clean before applying whatever you use. I recently bought an auction lot that included a two part aerosol product to protect polished dies in storage. Step one cleans potentially corrosive fingerprints and de-acidifies, the other part is a wax to protect.
Waxes are kinda neat, in that they form a fairly firm protective barrier - at least at non-extreme temps. Many of the military products seem to be wax based, and are engineered for indoor vs. outdoor, etc. Imagine protecting oil platforms on the north sea. I have a bunch of ancient Tectyl that I've been experimenting with. I like it a lot for some stuff. But the old age gives me concerns about pin holes, etc. I need to do more testing before relying upon it. Wax based products are also extremely sensitive to product temp and machine temp. Putting it on a cold machine can be a challenge.
For some important applications and surfaces, I agree with others in preferring grease. It works extremely well, is cheap and universally available. It goes on easy at any temperature. You can visually confirm complete coverage. Grease is peace of mind. Put a big glove on, and spread it, with a stiff brush for nooks. Seams can be completely sealed. There is no drying time. Covering the grease with a layer of plastic wrap, on large surfaces like ways or tables, will keep it from getting on tarps and help prevent it from being wiped away (though it is hard to completely wipe away).
The formulation of the aerosol grease products is hit or miss.
Any grime or dirt on the machine will tend to absorb and hold moisture. Some of those old deposits are not easily or quickly removed. What about your leadscrew? Any grime in the threads? How do you protect it? The wide carriage and short bed of the 10ee creates some access problems that don't occur with longer beds.
Consider the backside and inside of the apron, and the gears and half nut. They are exposed and it is really difficult to coat those. You might not want waxy or hard to remove products there, so maybe FF is better in that location? I've considered ways to tuck and fold a tarp up in there, then pull it down and out, up and back over the bed. You could include a wad of desiccant in that key area. Small magnets can help hold covers.
Clearly, to protect a 10ee we need to create an environment that is free from condensation at all times, but we also need to plan for the what-ifs.
How to protect the hidden sliding surfaces of the ways, cross slide and compound? That's tough. We've all seen lathes with rust where the saddle was sitting, and I don't believe it always relates to coolant. Be sure and lock the carriage so a bump of a handwheel doesn't displace protection on the bed.
Wood crates.. I am reminded of a recent machine transport story on PM where a machine (I think a Deckel) quickly rusted during transport. Questions were asked about import plywood and whether any acidic fumes, etc, could have been a factor. Newly purchased plywood may still be damp and outgassing fumes from adhesive and processing. Another option to plywood may be foil backed sheet foam? The lightweight makes it a lot easier to handle. It can also be taped together.
You can buy remote-read humidity and temp monitors. You could install one under the cover or in your crate, and have your caretaker periodically check the internal humidity. It'd be nice peace of mind. You can also buy cheap loggers, so you'd have an idea about transitory events.
Be sure the lathe has a moisture barrier beneath it, even on concrete. A sheet of plastic, etc. You don't want moisture coming up and getting trapped under your top cover. I've often seen a sheet of plastic get fogged with condensation within minutes of laying it on a piece of "dry" concrete. The 10ee has the advantage of having a fairly well sealed chassis on the bottom. You can snug up your top covers, at the base of the machine, with cling film or elastic cord. Mine has an electrical cabinet on the back that complicates sealing at the base.
Consider whether the machine is sitting on a slab of concrete that is going to freeze, and whether you want insulation from that surface.
Consider whether the coolant pump, lines and reservoir are completely dry. If there is any residual in there, it could be an internal source of moisture - remember when the Three Stooges would bolt the door with the monster still in the room?
Don't forget some kind of barrier on top in case the roof leaks, etc.