I don't do much car audio but I do electronics.. If you found wires going to
a missing amp there should be another set of wires going from
the missing amp. I assume one side would be RCA and one would be a bunch of speaker wires, but if both are speaker wires you'd just have to connect the wires to get continuity between the deck and speakers.
I'd start with a continuity check to see if the existing wires are actually connecting the speakers with the deck. From your previous experiments I assume that will be a no. It sounds like the next step is to follow either end of the wires in until you find the break. That should either be an amp that isn't getting the turn on signal, is fused out, or is missing.
Barring all that wire tracing, you shouldn't actually have to go all the way through the door to the speaker. Just find the speaker wires after they enter the truck by the door hinges and solder your new wires to them there. (or keep tracing at that point)
You should also figure out where the wires by the missing amp are going to, if they head out to the speakers, you'll just have to run wires to that
btw.. do yourself a favor and solder everything.. otherwise you'll end up with a mystery crackle in a year