Well I connected power to the two outputs from the LCM and the two reverse lights light up so there is no problem from output of LCM back to lights.
Would a faulty LCM just cause the reverse lights not to work and all others to function correctly?
I was messing with the switch on gearbox before(not today) and I disconnected it and probed it with multi-meter and it worked. I also checked power and there was power there full time. I did not check after I put it into reverse to see if power came out of it.

Also where would you go to download INPA?