Connect Gate Remote Board Directly to Arduino...?

Look in the PDF that is linked on the ArduinoInfo.info WIKI. Pin 1 is marked.

Pin numbers go Counter-Clockwise from pin 1. As seen from the TOP.

This is because people are used to going clockwise with pin numbers. On vacuum tubes. From the BOTTOM of the socket. Inside the chassis where you are soldering the filament transformer wires etc etc. In 1949. Everybody knows that 8)