Turn signal relay ?
I may be using the wrong terminology, Rob. The "module" I'm referring to plugs into the wiring harness just under the left side cover in front of the battery. The aftermarket replacement merely adds some extra resistance to compensate for the LEDs. I assume there is nothing else in the turn signal path?
If it's nothing more than a relay, I think you've answered my question.
Terry
I think what you have is in addition to the stock turn signal relay. It could be that unit also, but I suspect not because your running lights are working properly. I don’t know if I’d go buying a $50 OEM relay on a hunch. But you might be able to switch with another bike to see. I had one of those signal modules also, and really liked it. But it had an intermittent problem that I couldn’t fix and eventually pulled it. Your problem doesn’t sound like that is the problem.
Pulled out the aftermarket "module" and plugged in the OEM it replaced: Turn signals now work fine - just blink a little fast. Frankly, I may leave them this way . . . . . it's much more conspicuous.

Thanks, Rob - I appreciate the input.
Terry