The problem was the 1967 switch was fine in a Mustang with a single brake lamp bulb on each side. In a 1967 Shelby or Cougar there are six brake lamp bulbs. The fix was installing a 1969 Lincoln brake lamp switch as a service replacement C9VY- B which has beefier contacts that don't melt as quickly.
The Lincoln switch is the one to use for power front disc / rear drum brake applications.