Welcome to the wonderful world of the Ford water heater! You don't say what engine it is, so I'll assume it's the original style with the water pumps in the heads. These were never the ideal setup, Ford changed them out pretty quick, but they did work.
Check the top hoses for hard spots. The thermostats sat on top of the water pump and were held in place by the hoses, when the hoses get soft the 'stats can slip up into the hose where they can't work right.
Then there's always the possibility that the block is cracked. Fill the rad right full and start the engine. Watch the water in the rad, a steady stream of bubbles or water being forced out is a bad thing. Either a crack or a head gasket gone.
Do you know if the engine sat for a time without a rad cap or maybe no rad? Mice love dark holes like water passages to build nests in!