My run light on the right side does not work. The left one works and both blinkers work. I changed the bulb and still no run light. Not sure where to look next. Thoughts?

 

Year/model?

 

96' Softail Custom

 

Get your test light out and start checking for power at the contacts inside the socket. Then work your way back from there.
Just a suggestion ... it helps to let others know what year and model bike you're talking about and any modifications that were made.

 

Thank you I will try that. Thanks for the advice too.

 

Some sockets allow bulbs to be installed in two or more ways since the pins will align. Doesn't mean the contact points are properly alligned. Only one way works. Try removing the bulb and turning just so slightly to the next position the bulb will fit. It's worked for me a few times.

 

Being most running lights (I'll assume you mean aux. spots) come from the head light bucket then go from right side to left check your socket.
Now if you mean the running light built into your turn signal, you'll have to trace it back from the bulb to the connector under the seat or tank.

 

Light bulbs are sometimes bad, right out of the package. Try another.