The wiring circuit shows +12 coming from the fuse box to the reverse switch to the bulbs in the rear.
- It appears from that the backup light shares a fuse with the turn signals. So if they are working, I don't suspect the fuse.
- You don't say what trans you have but each have backup/reverse switch specific to them. I would test the switch. In my TH400 with console, the switch mounts on the shifter lever assembly within the console. Search in this forum for "backup switch" (use quotation marks) for discussions of manual trans.
- I would still check the rear bulbs and their holders. Bad bulbs and a bad ground to the bulb holder are common failures. They are easier to test and cheaper to replace or clean then the switch. I would take a multimeter and see if you get +12 at the light green backup wire by the light with the trans in reverse.
