I found the relay I needed on Amazon for $8.40. The relay was NTE Electronics R46-5D12-12.
I used a soldering iron and a solder sucker to remove the old relay from the circuit board. I soldered the new relay into place and it worked
The solder on the PCB had a high melting point which made removing the original relay a bit harder than I expected. In the end, it took me about 30 min. to make the repair.
Alan, do you have a schematic for the printed circuit board? How did you learn which relays controlled what?