Gound Problem?

[69CudaFB318VA]

  I have a 69 Barracuda fastback 318 w/automatic trans.  When driving the turn signal indicators on the hood glow dimly, and when parked and off, the interior light under the glove box glows dimly, killing the battery if left too long between startups.  Do I have a grounding issue, or something else?  Where should I start looking?   

[Bullitt-]

Wish I could say for sure but it sounds like feedback trough a shorted component.. Possibly the emergency flasher switch...something that has power full time.
I'd start disconnecting components one at a time until the situation clears then study anything past that connection.
Wiring Diagrams http://www.mymopar.com/index.php?pid=27   

[bandt]

Disconnect your ground cable from your battery. Use a multimeter switch it to DC amps. Put one probe on the cable the other to the negative on the battery if it shows 0 there is no draw. If there is a draw you can start pulling fuses one at a time. If you pull one and it shows 0 after that's the bad circuit you just have to figure out where it's grounding.

[69CudaFB318VA]

Thanks a lot.  At least I have a couple of places to start my quest to find the problem.  Will let you know what I find.