Heater doesnt work well or at all when you are low on coolant. They usually leak onto the carpet. Ive never seen a Tbird / Mark with a leaky heater core that leaked out of the A/C Drain, that is un-likely .. no reason to replace the Evaporator, they typically dont go bad like heater cores do and you would have to service the AC as well.
Check for white residue, its a telltale sign of leaking coolant if its not already obvious. Hissing sound from the passenger side .. I would start there.
Otherwise, fill it up, and get a pressure tester / adapter for the radiator. You can pressurize the coolant system and look for leaks ( UV light helps also, most coolants will glow ) .. or just run the engine and look for leaks.
If you want to check for a blown HG, do a compression test and a leakdown test.