Green connector is to power up the seat back heat, which I didn't know these seats had. Those are tied in now.

I am planning on splicing into the little brown wire at the original switch to go to brown wire on the new switch on the passenger side, unless that's not the right thing to do. Any thoughts on this?

Basically, on the switch, the gray wire and brown wire will tie together on the switches. The blue and red wires will go to the relay and the ground will just tie in with the rest of the grounds.