The same cutout problem developed with my '88 a few months ago. Would cut out when the high beams were turned on. Just turned out to be bad/corroded grounds. There are ground terminals towards the front on each of the inside fender wells. Just cleaned them all up and the problem went away. Or course alot of electrical stuff goes through the ignition switch but that's usually not a common problem. There's probably also some ground connections in the trunk for the rear lights.