Light switch problem

[youngcuda]

Nearing end of Gran Coupe restoration.  Problem: when I switch the running (clearance lights) on, the turn signal indicator lights on the speedometer both illuminate.  The clearance lights do go on but the dash turn signal lights also.  Is this normal?  Additionally, my turn signals blink kinda slow, and when I turn on the running lights or add the headlights, the turn signal lights are super slow.  Am I back to checking all bulbs and all grounds as the only solution?

[JS29]

 Could be feedback or it could be a bad ground. start by taking a parking light bulb out one at a time and see if the signal light glow go's away. 

[MEK-Dangerous]

Are you using LED lights anywhere?