Right turn signal works intermittently with the day time running lights on.

Sometimes the flasher unit gets weak with age http://www.napaonline.com/Search/Detail.aspx?A=NF_LF12_0131486427&An=599001+101996+50010+2010012 try changing it and see if it makes a difference

Check your flasher beneath the dash.

I had this same problem driving me nuts, and I'm an electrical engineer. The answer is, the idiotic turn signal socket sucks!! There is a loose connection between the ground terminal (outer ring of the bulb) and the ground terminal at the base of the socket. Two ways to fix: 1. replace the socket. 2. Take the socket apart and clean the contact between the base and the outer ring that holds the bulb. I chose option 2 which costs 20 minutes of fiddling with it because it was not meant to come apart that way.