Rear Right Break Light/Turn Signals
 

So my 78 Vette has had a problem since I got her. Her right rear brake light doesn't work...when the headlights are on. When the headlights are ON, the running lights work fine, but when I hit the brake, the entire bulb goes dark. When the headlights are OFF, the brake lights work, but the right one is dimmer than the left brake light. Also, when I use turn signals, the right one is much slower than the left.

Is this a grounding problem? I'm going out in the morning to make sure all the grounds are solid and corrosion free. I'll report back with what I find.

I should also mention that I'm running a brand new 1157 bulb.

What happens when you turn on the hazard flashers?

I think you might have a shorted out socket on the right side that's causing this weirdness, otherwise the running light filament is completely separated from the brake/turn filament.

Sounds like a classic ground issue. The brake light is using the parking light for its ground until the headlights are turned on.