Is this an indication of a bad relay? If so which one?
Thanks!

Nope. It's most likely a mis-wiring at the taillight buckets, or having the wrong bulbs in the wrong sockets.

Unless the brake lights are on any time the ignition switch is on--in that case, you put the washer on the brake pedal pushrod on the wrong side of the lever on the brake light switch.

--DD

Bad ground at the tail lights.

Courtesy of Jeff Bowlsby...

Click to view attachment

What is strange is that they were working before I went out one night and was turning the lights on and off for my kids. I didn't change anything. I'll check the ground-thanks everyone. Any other ideas welcome!
Also, I noticed that with the ignition off, and the lights turned on the brake lights are on. If I step on the brakes, it makes the gas needle move to position, and the voltmeter moves to on.

I double checked the connections on the rear lights, all terminals were clean and connected properly.
Could the headlight switch be the problem?

The latter sounds similar to some behavior we see when fuse #8 or #9 pops.

--DD