2009 Street Glide. Stock incandescent bulbs. I have the same problem just on my right side. INFO: All bulbs work and are good. THIS IS NOT a burned out bulb or a burned out element in a two element bulb!! I turn on the right turn signal and it will flash at the normal rate for three flashes and then starts to flash a twice the speed. I looked carefully at my front right bulb. The running element of the two element bulb works fine, but when I flash it the running element turns into the flashing element and the flashing element does not light up. I have switched left and right bulbs. Same result. The left (and operating normally two element lamp) has the running element lit and then the flashing element lights when turn indicator turned on. Left side flashes at normal speed. On four way flasher the left and right flash opposite each other.
Okay. So the TSM is quite smart. My issue was that the connector inside my fairing had partially worked loose. My fault for not reinstalling it properly. The flash element was not making a circuit but the running element was. The TSM used the running element as the turn signal. It would flash running element three times slowly then go to double speed. It will do this as well if the turn element (of the two element bulb) is burned out. The running element is less bright than the turn element. Look for it being less bright than the other side. So here would be TWO things to do to try and fix this misleading problem. 1. Ensure flash element is good (use DVM to check) or compare brightness to other lamp. You can actually get close enough to the lamp (yellow lens off) to see which element is flashing as well.
2. Check connector inside fairing to ensure it has not come loose.