By 'Lights' do you mean lamps?
If these are incandescent lamps (like torch bulbs) then I would expect them to emit visible radiation, on the other hand if by light you mean LED's then more than likely they would emit infra red and the 'receivers' (photo detectors) would be sensitive to that part of the spectrum, so not visible. One easy way though of checking if IR LED's are working is to view them through a smartphone camera when they would show up as a bright dot.
I am not familiar with Mitutoyo scales but even if you determine that the light source is not working, unless you have reasonable knowledge of electronics its not going to help you find the actual fault.
I have not re-read this whole thread again prior to this reply but is it now clearly established that the whole system works, except for one of the scales?
Ian P
Edit, I see Old Mart too, does not know what area the fault is in
Edited By Ian P on 16/04/2020 21:00:08