[Bargeld]

Switch in the gear shifter might be bad or come disconnected. This would prevent any signal for "reverse" going to those areas.

 

[Bargeld]

When you put the gear in reverse, regardless of it being an auto or manual, there is a switch/sensor that detects that you put it in reverse. Sounds like that switch/sensor isn't functioning.

 

[Bargeld]

Follow the wire, see where it goes. I know you say fuses ok, did you check both fuse boxes?

 

[Bargeld]

So 1 & 2 should have CONTINUITY when in reverse gear. No CONTINUITY in any other gear.

2 & 3 Should have CONTINUITY when in neutral. No CONTINUITY in any other gear

 

[Bargeld]

Just to be clear, when the manual says continuity, it means between between the 2 pins, not continuity with the vehicle ground. So when in R, you should take the multimeter and put red on pin 1 and black on pin 2, if there is 0 resistance (or negligible resistance), then the reverse switch is functioning correctly.