1) The front running light portion of the turn signals work.
2) When I hit the handlebar mounted switch, the selected turn signal light goes out but does not blink.
sounds like you need to rub dielectric grease on your signal-selector 'inside' your left handlebar housing especially by the #2 part. At least it worked for my bike. It's not my solution but the original poster on a different forum said something about the selector developing a film on the contact surface over the years. Dielectric grease might not remove a thick crust but it's worth a try if this glitch is recent. If the screws that hold your left clamshell together face up, it's worth while double checking the screws a day a week later .... just to make sure you put them back tight enough (I used med locktite on the threads). The screws are usually different lengths.