Just to clarify, the stalk turns on the high beams when pushed away from you (and locked there). Pulling them towards you is intermittent (flashing).
I don't think there is a way to service the high beam switches. Looking at the pictures I have from when I sold off my 3 way turn signal switch, you can see that the high beam switches are part of and buried deep inside the turn signal switch. It might be possible to remove the turn signal switch, drill out the rivets holding the parts together, and get inside, but I've never seen anyone do this...