Help wiring motorcycle turn signals?

I'm trying to mount aftermarket from signals to my triumph thunderbird. The current system is a 2 wire system. I noticed that the turn signals that I bought are for a 3 wire system. Can I still use them? If so, do I just connect the running light and signal light to the Positive/signal terminal on the bike, or should I tape off one of the wires on the turn signal?
Thanks!

I figured if I tied the 2 positive wires together it would make the bulb brighter since both filaments would light up... But I guess that's not true.. or not a good idea?

Those signals use dual filament bulbs (running & turn signal).
Connect the signal's ground wire to ground.
Test the other 2 wires and only use the one that lights the brightest.
Tape off the remaining wire.

Wiring the 2 filaments together will not make the bulb brighter.
That's like using the headlight of a car and adding a wax candle - the candle won't make any difference.
The downside - using the 2 filaments will draw more amps and the flasher relay won't be able to handle it (the signals won't blink).

I agree with guardrailjim.

It would be possible to connect the the two hot wires together, then tie these into your bike's signal wire. There's not much benefit to that, though.