1969 cutlass S gas gage works perfect except when I turn on head lights then it drops about a 1/4 tank from where ever it is turn lights off and it goes back any suggestions

 

I'm guessing a bad ground to the gauge that is shared w/ the dash lights. Adjusting the brightness of the dash lights may cause the gauge reading to change too (have you tried this?). If it does, I suspect that confirms a bad ground is the issue.