On my 2002 Classic, the turn signal relay was under the seat on the kickstart side; though I don't know if they moved it in later years. I just had to replace mine last week with a new one. The signals themselves and the indicator light in the speedo all started staying on pretty solid and only flashing intermittently when either of the turn signals was engaged.
The factory relay is a small black plastic block about the size of 3 pieces of bubbalicious gum. I tried my local 'we sell/service all brands' motorcycle shop and new relay was $10. They are pretty universal, just specify that you need a 2 prong 12-volt flasher relay. Like ChuckD was saying, the two prongs are at 90-degree angles from each other and connect to an L-shaped wiring harness. Installed new relay and signals are back to normal.
Good luck, and I hope yours is an easy fix as well.