Headlight Issues
I would guess the hi beam indicator is actually a separate problem. The clusters in these girls are only grounded by the mounting screws. If the cluster becomes partly ungrounded, you can find silly stuff going on.
Start by replacing the dimmer, they are not expensive. Then monitor the voltage to the hi beams side and switch it back and forth while observing the voltage at the dimmer hi beam terminal as well as the behavior of the hi beam indicator. If there is no voltage, and it still glows, then the lamp is getting power thorugh the lamp shell.
I would also check the ground for the headlamps. They are all (normally) tied together to just one ground lug, somewhere on the radiator support.