Need a little bit of wiring assistance

Most of our light fixtures do not have actual ground wire. Those mounted in plastic grilles have a ground wire. For all others...The base of the bulb against interior of socket, the socket to fixture, and fixture to car body. That's the ground path. Rust inside the socket can cause no light or weak light as can any weak metal to metal connection.
Hope you checked fuses with test lamp or meter 'cause just looking at them doesn't always work. Sometimes the link is broken underneath the metal cap on glass tube where we can't see it. Then the clips in fuse box are sometimes so rusted that continuity doesn't happen.
The reverse lamps are likely powered by radio fuse ( I would have to go to wiring diagrams to confirm ). Reverse lamp switch may be the fault. It's screwed into the transmission.