Oh, slight possible, check your headlight relay and/or fuse. If it in relay, easy two wire-fix, but it means a separate switch, cuz ya have to bypass the relay into two parts.
if you have a 95-99 cav then if your daytime running lights are your high-beam with less voltage so they are'nt as bright. If these work then it would be the relay for the hi-beam.
__________________
Red Z24 = Dead, 03 2 door = 15.5 with no traction. low 15's here i come
I am having the same problem with my 98 cavalier. I have day lights but no head lamps, however my brights will come one, but they won't stay on by themselves I have to hold the switch back with my hand to keep them on. I have checked my fuses and the bulbs are not burnt out, I think I may need a whole new switch. If so how difiicult is that to replace. Also my care radio and clock reset every time I turn the ignition off.
I had this problem twice with my 2003. First time it was a broken wire somewhere near the battery. It was fixed under warranty. This last time it supposedly was a corroded connector.