The hot water flow is controlled by the double solenoid valve thingey you see just in front of the battery.
The valves are controlled by the module you have already replaced and supply a ground to either/both valves to actuate.
The valves are supplied 12v via fuse 15.

I think the valves work bass-ackwards of what you'd think ( read that somewhere ), IE energizing the solenoid stops the flow, but I could be wrong, never verified this, too messy.
( try pulling fuse 15 and see if it goes all hot/cold )

There is also a thermister in each left/right heater core that tells the control module what's happening there.

NOTE: would you be willing to part with one of the control modules at a reasonable price ?