Always check the obvious first- are you sure it isn't the bulbs? U can test the sockets for 12V on the high beam side to see if you're getting power there.
Do you get the blue high beam light on the dash when on high beam?
Could be the multifunction switch too- not uncommon for them to fail.
Not sure if there is a relay, but if there is, just switch it with another in the box instead of buying one. If it fixes it then go buy one.