Electric Gremlins, My tail lights are crazy... Options

[Carlitos Way]

er, not MY tail lights, my car's tail lights.

I'm trying to get my car up to "roadworthy" conditions. I just purchased it and the PO didn't inform me of the electrical gremlins.

So, I have a weird electric problem:

When I switch off the ignition, if I "accidentally" activate the left turn signals, the right rear tail lights light up, and stay on.

Also, when I was testing the hazard lights, a funny thing happens. The left and right lights do not light up at the same time. They light up in alternating patterns... so it's kind of a fun show... and it reminds me of a few too many late nights with red lights shining in my rear view mirror.

I'm guessing I might need new relays but before I go spending money on 3-4 relays, I'd like to get more input.

Any thoughts or suggestions are welcome.

Thanks,

Carlos