When I try and turn on the Brights it shuts the Headlights Off? Any suggestion on what to investigate as the probable cause?

 

Welcome to the forum.
Not sure but I would suspect that there is a relay in that circuitry that might be causing the problem. Some of the aftermarket suppliers such as Wilcox, Corvette Central, Zip Products, sell a wiring diagram. Another alternative is to get a copy of the factory service manual.