Good point 97 SL320, more specific troubleshooting needed..Maybe using a continuity test/ohm meter on that headlight circuit for both shorting and for the ground resistance. A badly grounded or weakly fed headlight isnt going to drop the voltage to the systems and cause cut out..just a dim headlight, right? But one which is shorted from the positive feed just might do it..Esp if the alternator is failing..It could actually be at the fuse..which corrode on these cars. And left and right have different fuses if I recall. Others are far more accurate in the systems details than I am..

Hope to hear the conclusion..