Al:
A bit of quick math shows your lathe has what are known as "16 pitch" gears (16 pitch refers to the diametral pitch). Finding actual Seneca Falls lathe parts is a very long shot, if you can find someone parting out a Seneca Falls lathe. 16 pitch gearing is quite common. I cannot say what the price would be, but if you look at stock gearing (known as "spur gears) as made by Boston Gear or Martin Gear, you may be able to find replacement gears. Often, these stock gears are sold with a smaller 'pilot bore' thru them. It is then up to the purchaser of the gears to bore them to final size and put in any keyways or set screw tappings required.
You can also check on eBay, making sure to note "16 pitch spur gears". I suspect the Seneca Falls lathes used gearing with a 14 1/2 degree pressure angle, which was more common back when your lathe was built. There are two common pressure angles: 14 1/2 degrees and 20 degrees, so be sure of what you are buying.
Boston Gear used to (and may still) offer 'lathe change gears". These were cast iron spur gears in various pitches/tooth counts.
The other alternative is to have new gears made. The traditional 'one off' method of making spur gears was to use a milling machine, gear tooth milling cutter, and a dividing head. Not the world's most accurate means of making a gear, but OK for an old lathe's change gears or quadrant gears. A more modern method is to find a shop with CNC Wire EDM. They can cut the gears quite accurately from steel plate using CNC wire EDM (CNC = computer numerical control, EDM = Electro Discharge Machining). Another option is CNC waterjet cutting if the right person is programming, setting up and running the waterjet.
The other option is to find an industrial surplus store where all sorts of machinery and equipment and other stuff like fasteners, pipe fittings, odd cutoffs of metal stock, motors, pumps, kitchen sinks, old medical apparatus and anything else is sold. These places have anything and everything at one time or another, no knowing what they have or when. There is an industrial surplus place near me, and they had bins of spur gears for some time (all gone now), and they have bins of tangled together springs, tons of nuts, bolts, socket head screws, random heaps of bearings, old medical equipment, and on it goes. Find a place like that and bring a mating gear to compare and 'roll into' any gears you find in this kind of store.
Other suggestion: get a used/older edition of "Machinery's Handbook" if you want to work with old machinery. A newer edition of Machinery's Handbook is pricier. For basic gear formulas and much else, an older edition will do you just fine. There are empirical or 'cook book' formulas to walk you thru gear design and figuring out what pitch gearing you are working with if confronted with existing/unknown gearing.