I don't see any heater hose that runs to the back of the engine. The photo below is from a 86 Town Car, and the red hose running to the pipe at the back of the engine is part of the smog pump (emission) system.
The part that the hose to the rear of the engine is connected to is a air check valve.
Notice the image below, you have the inlet heater hose coming out of the front of the intake running to the blower thermal lockout switch. From there is a small piece of heater hose that continues on to the heater core. Then the other heater hose runs out of the heater core on to the water pump. Other than that, all that's left is a bypass hose at the water pump and your two radiator hoses. That's all the hoses that carry coolant unless someone has changed something. Just go to the auto parts store and buy a small piece of heater hose to connect the blower thermal lockout switch (sensor you are talking about) to the heater core.