I would replace the headlight switch. I was having the same issue on my "58, the rheostat was severely corroded and not allowing any current flow. The high beam indicator is on a completely separate circuit than the dash and dome lights.
Thats what I would do. After getting a can of Deoxit and cleaning the contacts/ on the switch.
Does the switch have a fuse?
Those are pretty tough switches. I have 2 old ones that sure don`t look like they would work but do.
