Just for fun, put in one new bulb to see if it works.
I don't really expect it to, but you need to eliminate that as a possibility.
Grab a piece of wire out of your junk drawer (or wherever you keep your spare wire), connect one end to ground somewhere on the frame and tuck the other end between the bulb and the socket - along the side of the bulb (don't let it touch the contacts on the bottom).
If doing that makes that particular bulb work then you've got a bad ground connection somewhere.
I had my brake lights go dark on my '94 Bounder. There's a relay under the hood that had gone bad. Replaced that and all was good. Had to cut back the wires a couple inches and put on new connectors too. Corrosion on that old of a vehicle is a challenge. It affects the grounds as well.
'02 Winnebago Journey DL, DSDP, 36' of fun.