On NZ spec '84 AE86 the heater tap is cable controlled from the slide.
One hose in connected to the RWD water pipe that runs from the back
of the water pump. The other hose connects to the outlet from the
thermostat sensor block on the back of the head. The tap is mounted
up high on the firewall where it is easy to see.
If you can manually operate your valve, try it in both the "open" and
"closed" positions with the engine running and at normal operating temp.
If this doesn't give you heat, then you have a blockage.
Hot water flows from the thermostat sensor block to the tap, then to the
heater core. I am assuming the the type of tap is the only difference in
the plumbing... maybe you have climate-air ?? Flaps will be to control
where the air goes... recirc, screen, vents etc., and should not have any
affect on the temp of the heater core.
If you have
green water in the hose after the tap, but
not green water
in the hose coming from the heater core back to the water pump, then
the core is blocked

But check that you haven't twisted/crimped/kinked
a hose under the dash when putting the heater back in place. Hope this
helps
Cheers... jondee86