Connect Gate Remote Board Directly to Arduino...?

I've done this before open the case of the remote and find if the buttons are high going low most time that the case I then soldered a NPN most any work I had 2n3904

solder the collector to the high side and emitter to the ground side put a 1k resistor on the base
tie the ground of the remote to the ground of your arduino and hook the 1K to a digital pin.