High beams blinking

Your description sounds like there is a partial short in the wiring to the high beams or a ground is bad and they are grounding through the other lamps, both can cause excessive current draw. To check if it is a ground issue the easy way would be to remove both of the headlights from their respective sockets. Now on each one there is a black wire that is the ground for the lights. Simply run a jumper wire from each one to a good ground, then turn on the high beams and see if they still have the issue, I suspect they will but if it has suddenly stopped start inspecting the wiring where it went through the housing to the wiring harness, you are looking for damage or chaffing that would show it rubbing through. If they are still an issue and you find no damage, start tracing the red wires as those are the high beam lamp feeds, one goes back into the dash to light the high beam indicator, any of them could be the issue though. You may want to get a short finder and use it to trace the wiring. The simple version uses a small meter and a circuit breaker to pulse the power in the wiring and you use the meter to follow the wire and watch for the needle to stop or change direction. These are sometimes available as loaner tools at some parts stores as well as the nicer electronic units. Once you find the area of the short you would simply repair the wire or wires.