Suspect he meant 0.0001" per foot or some similar archaic measure. That would be more like 1.72 arc second. There's a DigiPas inclinometer that claims 0.2 arc second resolution, and 2.0 arc second seems to be available from several sources.
Assuming you mean ~.0001 in/ 10in (roughly 2 arcseconds), this is comfortably within the territory of standard electronic levels using galvanometers or LVDTs. If you want new, Talylor Hobson and Tesa/Wyler both make quality options (though they aren't cheap). Search Talyvel and Niveltronic, eg:
Taylor Hobson Precision Clinometers and Talyvel electronic levels used for precision angle and level measurement. Key application is flatness of surface plates and granite tables
If you're open to used, Federal also made some good electronic levels, and of course you can save $ buying an older generation Talyvel. I have an early Talyvel that would meet your spec and was ~$500 used, if I remember correctly.
I have a friend get the DigiPas level mentioned above. He used it for roughing in CNC machine level before finalizing with bubble levels. He wasn't smitten with it, but being able to read the level using his smartphone really saved a lot of climbing around the machine.
FWIW when Okuma had factory techs level a large VTL at my work, they used spirit levels. I offered some electronic levels to help them and they said the factory requires that they only use bubble levels for machine setup.
There aren’t many jobs that require a level that is in the 0.0001” in 12“ bracket. I had a 0.0001” in 10” spirit level and I sold it. For general shop use it took too long to settle. Having said that an electronic level will give you an instant reading. I found a 0.0005” in 10” level was plenty good enough for most machine tools.
The 0.02mm/mtr are commen in metric land You can read 0.01/mtr or better if you buy one with a long bubble You are really sure you want more as double the accuracy ??
Don`t leave any smell on your hands when you clean surfaces then
I have used one of the old Federal levels. It had two read heads, and could be used as a differential level. It also had different levels of resolution, so you could set the level of discrimination desirable. At the highest resolution, it is common to detect floor movement.
Your requirement of 0.0001" in 12" corresponds to 8.3 parts per million. For comparison, one arcsecond is 4.8 parts per million. So your requirement corresponds to an angular precision of 1.7 arcseconds.
One way to get that reliably is via Talyvel electronic levels. The Talyvel 1 and 2 typically go down to about 0.5 arcseconds of resolution and similar accuracy. The Talyvel 3/4/5 have a resolution of 0.1 arcseconds and accuracy of 0.2 arcseconds +/- 2%. A search on this forum with "Talyvel" as the subject will get quite a bit of additional information.
During the past few years I have reconditioned and sold several Talyvel 4 electronic levels - I'll have another one for sale in the coming months. That is a differential level with two heads, which is extremely useful if you need to evaluate the straightness or flatness of a surface (example: a surface plate) which shifts as you move around. Please drop me a note if you are interested.
Apologies for the slow reply, I just saw your PM and will respond shortly.
I have never worked with a Talyvel 6, so can't answer your question with any confidence. But from looking at sales literature it appears that they have taken the mechanical mechanism of the heads (which is identical for all Talyvel models) and grafted a small electronics module onto the top. This probably contains an IC with a differential inductance (LVDT) to digital output, and a bluetooth module for communications. The remainder of the signal processing and data reduction is done on a laptop which communicates via bluetooth with the head(s).
I do have two heads but plan to sell them as part of a complete set with the Taylvel 4 display unit and cabling. Details in my PM.