Dash light issues

[bw396ss]

My 68 has developed an issue where the dash lights seem to dim and the turn signals will glow when the headlights are on. Also when this happens the fuel gauge reads empty. As soon as you turn the head lights off or turn the headlight switch fully clockwise (shutting off the dash lights), everthing returns to normal including the fuel indicator. The clock also works just fine and the headlights, etc., are unaffected.
After looking at the wiring diagram I cannot see any direct connection between the fuel gauge and the dash lighting. I guess if some thing could shorting out the fuel gauge, but it is not clear to me how.
Any idea?
Thanks,
Bill