Okay, matching your description of the connector up, that's C107 and is for the power windows. There's an error in the FSM in the back that ID's this as a 6 pin, it's an 8 pin. You could (if you cared) check pages 130-131 and see that the 7 wires match.

There's no connection between this connector and Fuse 12, so its earlier behavior was a red herring.

Have you disconnected the cruise control switch on the column?

You may also want to remove your instrument cluster and check that out for burned traces.

Can you actually see when it blows via the gauges failing since they're off the same fuse? [Watching your cluster while braking is not a great idea, so you might want an assistant so you can watch the road.]

I would also check brake fluid, and the brake wear sensors. There's a path through to ground via the brake fluid level sensors. If they're low, and the problem occurs under hard braking, maybe it's there. Likewise with path to ground via the wear sensors.

You might also try removing the hazard switch from the console. In theory this should isolate the turn signals from fuse 12. You'd be without signals, but that would mean you drive like other idiots who don't use them.

Another option might be to unplug the warning module (like a relay). This, in theory, should isolate the warning lights, the alternator, and maybe some other things from fuse 12.

Continuing that idea, proceed on to the Top Dead Center amp (?); then maybe the cluster itself. I don't know if you NEED a TDC amp to drive, maybe just for the tach? Maybe not speed, but RPM related? Sheet 4 on the pdf.