I suggest sticking with connectors and not just splicing the wires together.
You'll need the
male 2 pin HB .050 turn signal connector, third one down
here. You'll need to crimp the terminals onto your bare wires, insert them into the connector housing, and then plug it in. It comes with two terminals, you may want to get some spares, they're small and not easy to crimp. You do need the male one, it refers to the terminals, not the housing.
Edit: you'll need to cut those ends off the bike wires, don't know where they came from, but they're not stock.