I had the same issue. Dims worked, brights didn't, but the indicator did. The only time the brights worked was when I pulled it in the garage to track down the problem. Frustrating! I replaced the dimmer switch with an NOS switch, but that didn't help.
I discovered that the high beam terminal on the headlight switch was loose in the switch body. I replaced the switch with one of my three spare headlight switches. Two of my spares had bad high beam terminals. One was burned right out of the switch.
Check and/or replace your headlight switch and then, as Jerry suggests, run relays. That will prevent the the headlight current from running through the headlight switch.
