Wiring issue with Wyze Thermostat no circuit board in unit

I have an ancient Day and Night A/C-Heater that had a mercury switch. The unit does not have a control circuit that I can see. It has relays and a transformer and other devices. The thermostat has 4 wires, with a fifth wire in the wall not being used. There are 4 wires from the thermostat to the unit with the 5th unused. When I go through the setup for 4 wires, it wants me to connect the c wire on the adapter to the c terminal on the circuit board. Since I have no circuit board in this old unit, I am uncertain where to connect the c wire from the adapter into the unit. I did some research in the forum but am still befuddled as to where to connect it to. Also, can I utilze the blue extra wire somehow as the c wire.

Welcome to the forums! Did you do the compatibility checker on the thermostat shop page? It said it was compatible? Able to provide some photos of the setup? I’d hope some thermo-gurus can pop in here and help ya out. Thanks!

Thank you. I ran the compatibility tool and it said my system is compatible. I will post some pics. I appreciate your help.