without knowing where the front lights ground, i'll take a guess.
i've fixed many strange electrical problems like this in other cars by cleaning grounds. first head light ground, then panel the lights are bolted to. signal light socket's themselves. new turn signal bulbs.
there was one time i had to clean where the bumper brackets bolted to body. seems like the headlights are using the signal ground. do the signal bulbs have a very dim glow when head lighs are on? maybe clip a temporary ground wire from battery neg. to signal bulb socket with signal and headlights on. move the ground to a few differant places.
grounds cause very strange problem
good luck rich

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88 300E White, sold 9-04
88 190E Black 2.3 sold
90 300CE White, Grey sold 12-24-04
92 400E White,Grey Sold 5-06
90 300CE 91K Signal Red,Black Sold 2007
1989 300CE Smoke silver,Tan Sold 1-08
1993 300E 3.2 M104 motor
1991 300CE White,Grey
1994 E420 beautiful car,gone to new home
1994 E320 Smoke an Parchment.Beautiful car