Ok , a real shot in the dark. The center high mount, has separate power from the front of the coach, to keep it operating when the turn signals are on. The brake light wiring runs up the steering column and the turn signal switch interrupts the brake light power and supplies power from the flasher instead. Turn signal switch wiring connector.
Just thinking and typing at the same time here. Every thing I think of , the speed factor throw a monkey wrench into.
Supplying power from the center to the outer brake lights, would over ride the signals, not good.
The only area where speed could be a factor, would be around the brake light switches, with wind from the left front wheel. I'm thinking my coach here , is your brake control ( foot valve ) under the floor?
If so , I'd be tempted to run a new wire from the brake light switches to the base of the steering column and hook it into the turn signal switch wiring. If there is a splice in the existing wire for the center light power, it could be that any movement of the under floor harness ,at speed , is causing a poor connection and allowing limited power past that point.
Like I say , shot in the dark.
For a test you could wire in a volt meter to the wiring at the base of the column and see if your getting full alternator volts when you apply the brakes at speed.