How can I add a relay to the manual control for my HVAC unit?
The wiring for the empty terminals is likely behind the board you can see, connecting the terminals to a common source, probably power, but not necessarily.

You will want a normally open relay for all but the 1A function, so that no power is required for the stop condition. For any given function, you'll need separate poles for each of the states that are different than stop. For high heat, you need a normally open 4 pole relay, or a couple double pole relays. When powered, close 3,4,7, &amp; 8. That takes care of the HVAC switches. How to power the relays from an IR/RF signal, I've no idea, except that it's done all the time, so should be just a matter of finding the right hardware.