1999 Lincoln Continental Losing coolant from overflow tank

When you say "leaks out the overflow tank", I'm assuming you are saying the coolant over heats and boils out of the overflow tank.

But I need to know of you replaced both head gaskets or just one? Also, did you pressure check the system?

If so, then something has failed. Either the water pump, the belts aren't tight enough, there's a leaking intake gasket, the fans aren't coming on, there's air in the system, or a blockage in the system, and finally, the thermostat is stuck closed.

You can easily check the pump by squeezing the radiator hose while someone revs the engine. If you feel the pressure, the pump is working. You can test the thermostat by feeling the temp of both hoses as the engine reaches operating temp. If both hoses are hot, the thermostat is open. If one is and the other is cold, then the thermostat is stuck closed.

The fans should come on as the engine reaches temp. If not, check the relays first, then the fans. You can also try bleeding the system of all air.