Turn signals do not require a special connector. They can require a resistor to make them blink and the correct slower speed, but that doesn't hurt anything. I've had my aftermarket lights blinking too fast since 2007 and probably about 100 miles on the bike.

 

Hmm, so when you say the 'main' fuse are you talking about the red 20Amp (or 15 - whatever it is)? If thats blowing you have a bad earth/short in your wiring.

Have you checked the other fuses the 5/10(?) yellow and green ones?

I think the connecter you're talking about is the same as i used, that go between the new turn signals and the old wiring. You can get away with those if you do as boredandstoked suggests by using a resistor. I used the connectors and would have swapped out my turn signal relay (so they would flash normal speed) - but there was already an aftermarket relay fitted that worked. When i swapped my old TS's for LED's i wired the connectors the wrong way and blew my TS fuse, i just swapped the connecters round to the right colour - (stupid Chinese colour coded wires) replaced the TS fuse and all was good. Check those (green/yellow) fuses in the main fuse box and see if they're all good. Replace any that have blown, re-wire your TS's to the correct wire and then turn the ignition on - everything should work, if any of the fuses blow or something doesn't come on - you still have a problem somewhere.