I don't know a lot of specifics on the Camaro's but if the headlights and front lights have dedicated grounds and they are all on the radiator support then possibly the radiator support being bolted to the fenders and then to the firewall are not electrically sound ?.
I've seen some GM's with the pigtail for the battery negative bolted to the fender and sometimes if the fender, radiator support, and firewall are painted heavily, they may be solid mechanically but electrically poor.
If the front lights work with the headlights off and then when the headlights are turned on, maybe the ground is poor and now everything is being shared but I would think in that case the headlights might be somewhat dimmer but who's to say without a reference brightness to go by.
Maybe too try running a test jumper from the bulb socket or the housing of the bulb to the battery negative terminal and see what happens.
I've also seen light sockets crimped to housings and while it might be mechanically solid, electrically it's poor.
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