Probably a bad switch, but are your fuses good, not just LOOK good? Replace fuse first.....then
Put car in air. Drivers side has speed sensor and anti-reverse lockout, and dreaded skip-shift . Passenger side Trans, half way up, amidships, is the backup lite switch.
1) Unplug switch
2) Determine if power to switch, key on. (test lite)
3) If powered, Jumper across and see if backup lites come on.
4) If lites come come on, its either:
-- a bad switch, (easy) or
-- a bad connection inside the trans. (worse)
5) If no power or lites, then the fun begins. I hate electricity.....Wires contain tightly packed smoke particles trying to get out. I have proven this !
Easiest: You could just order and replace the switch....cheap at MSRP from your local dealer of $25 p/n 4626593
WARNING: COMMERCIAL MESSAGE: Or $20 from PartsRack !