You can twist both wires together and crimp a ring connector to them, but I would fuse that the toggle power wire too - Just to be safe. Connect that lead to your battery + clamp bolt. Make sure the grounds on the fog lights are good too - if you haven't already.
So it seems that I might have the toggle wrong in the pic above so it might be ground side switched,(pin 86 and 85 are opposite).
Make sure both circuits are fused. Here is another pic. inline fuse holders like that one are a few bucks at the parts store. I just put one in for my LED bar.