Alright, after some testing the bottom line is that the high beam circuit is working.
I tested the ground connection, coming from the DRL module, and it tests out. With the high beams on, and the DRL module in, the high beam circuit does not work. However, if I remove the DRL module and turn the high beam circuit on, I get 14v going all the way to position 5 of the DRL module. If I put a jumper from 5 to 6 or 5 to frame ground or 5 to battery negative, the high beams come on.
So at this point, I'll assume that it's the DRL module that's issue here. Again, I put the module on my variable power supply, along with my multimeter, and everything tests out voltage and ohm wise. Obviously, I can hear the relay switch when the power is supplied.
I'm gonna put in a new module and see if that's the kicker. It's all very odd that it appears to bench test fine but has issues closing that 5 & 6 position to complete the high beam circuit.
Note here, the 14v at both pins of the LH high beam lamp through me for a loop for a hot minute. After looking at the wiring diagram, it makes sense now being that the RH high beams are tied into that circuit, which runs to the position 5 of the DRL module. It makes sense to have it built that way so that if a high beam lamp goes out, it does not effectively kill the circuit.