2000 Lincoln Town Car Cooling fan

Working from memory.
The interface plug for the fan is 3 conductor,
One wire a Ground
One wire normal speed
One wire high speed may be used with AC or if normal speed is insuficent. I expect you have an over heating problem more so if AC is on?
There are relays and fuses under the hood for these.
Check them, High and Low are seperate relays and perhaps separate fuses as well I expect thay are labeled perhaps on the relay/fuse box cover. If you have an ohm/volt meter this would eliminate much guess work.
Is the fan working while in the car at all?
Remember to check resist to Ground @ the plug
Hope this was some help not too late!