I suspect that there is a weak connection in the brake light circuit that is opening up under full (6-bulb) load.
Is this a factory disc brake car? If so, there is a 2-pin jumper from the brake switch to the harness that fails.
Unplug the red connector and apply 12V directly from the battery to the green wire on the controller…
You should get 4 out of the 6 brake light bulbs to light up.