I have a 1989 Chevy Cavalier with the 2.0-liter engine and an automatic transmission. I have water coming out of the little right angle rubber hose on the firewall below the A/C lines. When I put water in the radiator, the water just runs out of this tube.
This is strange to me. I thought the A/C system and radiator were different systems that are unrelated. I have the head off now and would like to fix this while the car is disassembled since it has already caused overheating.
Maybe you shouldn't be attempting the cylinder head job if you don't have a significant amount of automotive experience. Coolant coming out of the evaporator drain tube means the heater core is leaking and requires replacement.
The A/C evaporator and the heater core are parts of two different systems, but they are located right next to each other under your dash. So coolant leaking from the heater core will exit at the evaporator drain just like the normal condensation from the A/C system. You might want to get some help with the cylinder head and the heater core.