Front or back?

Front, ok that's 3 wire or 2 filament.  It's like 2 lites in one.
One wire turn one lite on, another turns the other lite on and the last one is the ground or the way electricity runs back to the battery.

Harley D decided to save money when he built his bike and he uses the frame instead of that 3rd wire.  So those 2 wires on the new signal are to turn the 2 lites on and the electricity run's back on the frame.

You can make a 3rd wire and hook it on the frame of the lite cause Mr. Suzuki decided to make his bikes cheap by selecting steel that rusts.  And he has to paint the metal, which isn't good for electricity.  And it can't run back to the battery very well.

A carpenter? that's easy... turn the ignition on, turn the lites on, lick both ends and stick em together.  

Get some wire the same size as what's already there (14 gauge I think) and strip the ends.  Attach it to the new turn signal inside the case by screwing or soldering it to the metal frame.  That is your ground wire and will attach to the black and white wire on the bike.  The grey wire is your running light and the green is your turn signal on the right side.  On the left the turn signal wire is black, I think.  Hook those up to the red and black wires on the ts.  If the running light is brighter than the ts then reverse the red and black so the ts is brighter.  That should do it.

Sorry, I missed that we were discussing the rear.  Add the same ground wire and attach it to the bike's b&w wire.  Then wire both the red and black wires to the bikes other wire, green on right and black on left.  

This is all assuming the turn signals are wired like a two filament bulb.  If they're not then just go bike's b&w to ts black and bike's green (or black) to ts red.  You won't have the option of running lights.