If your tail lights work you don't have a big strap problem. Understand you have one housing, one lens with two sockets inside. Each bulb is a single filament NOT a dual filament, correct? I see two power wires enter housing, one from stop switch, one from tail light fuse block.
Please advise: When you test the BRAKE light socket (not the contact) does it have continuity to the tail light socket? The socket is the part that the bulb fits down inside. The part that the bulb case pins touch.
Obviously these two sockets must have continuity, so check that. Touch one socket with one test lead and touch the other socket with the other lead. Any ohm reading is continuity. Set meter to "continuity". If there is continuity between sockets, I resign.
If there is no continuity between sockets and you said both contacts are live then:
With brake switch activated, Touch a wire to the BRAKE bulb case (the case of the bulb is the brass part with locking pins), while bulb is in, and touch other end all the way to battery negative post. You HAVE TO establish a ground to the side of the bulb by BYPASSING every wire, every bracket, every housing, every socket, everything, in order to start somewhere. The case of the BRAKE light bulb needs to be grounded by you in this way. IF there is 6V at it's contact, bulb will light. Remember: bulb is IN the socket during this test.
Please report the results of these exact tests. This is not that hard to diagnose. I may not be communicating properly or not understanding your tests.
I am pin pointing you to exact tests now. No other tests. I have clarified my terms so we are talking about the same things. Let's forget housings and brackets and the strap you found for now. Unless there is an unknown dedicated ground wire to the battery, your chassis is grounded. Your problem is localized at the socket. It's simple, each socket needs power and ground. Power to the center contact, ground to the socket and into the bulb case.
The fix is next. After the bulb lights.
Not sure about this:
"Confirmed end of wire has voltage with a meter when pedal is depressed."
"Hooked up wire to correct wire coming out of tail light assembly."
"I thought, perhaps, the assembly itself or the wire feeding it was bad. Checked resistance from the tail light assembly wire to the terminal inside the bulb socket and the meter pegged."
Does this say there was voltage on the end of wire at the tail light? The wire going to the contact in socket?
If so; instead of checking the terminal inside socket for voltage, you checked resistance between wire and the terminal inside socket? If so; that should prove terminal "would have" voltage. But you still need to actually check that the contact does have voltage.
This whole thing could be you just need to sand paper the socket wall and the contact terminal. The above tests will tell.
