Painless wiring brake light gremlin

I would get down to basics and "jig up" and test the TS switch(s) both for function and for how you have them wired

Get the factory diagram for the TS switch and draw out the original wire colors

"Truth table"

You have three power inputs:

Brake light switch power, hazard flasher power, and turn signal flasher power

Flasher power hot all time, TS hot with key in "run" and brake light hot with pedal depressed. Those should be easy to verify

Now with TS switch disconnected, use test light or ohmeter, switch centered, hazard off.

Only continuity you should have is brake switch wire to left and right turn should all be connected

If you turn on hazards, the hazard flasher wire should show continuity to both front and both rear turns, and I believe also the brake wire

With switch in left, brake should ONLY go to right rear. TS flasher wire should be connected to front left and rear left.

IF that all pans out, leave switch disconnected, and get a clip wire connected to power. Jumper power to the harness so as to power up the lights one at a time, make sure nothing is "crossed" in the harness, IE apply power to right rear, right front, etc Make sure that all works.

Even though you claim TS switch is new I think they are either defective or mis-wired