The fluid is pink instead of red for the cooling fan in my 2000 lincoln ls v8 I siphoned off the the tank and replaced with new fluid and it soon turned the same color

Fuse box diagram.
https://www.autogenius.info/lincoln-ls-2000-2006-fuse-box-diagram/
Some good info on fan operation of you car on below link.
https://www.justanswer.com/ford-lincoln/7k3bc-lincoln-ls-05-lincoln-ls-cooling-fans.html

Just a thought: If you have two electric fans one comes on when you turn the A/C on the other does not come on till the car reaches normal operating engine coolant water temperature.

the fan motor is going to need replacing. u have to take out the fan assembly along with the reservoir and the pump.

There is no relay on the cooling fan circuit.
If the cooling fan is not operating, check fuse #105 (20 AMP), in the underhood junction box, right front of engine compartment.
If fuse is good then test to make sure fan is getting power.
If no power then could be bad cylinder head temperature sensor, hydraulic fan solenoid, a/c cycle switch or the PCM.
If it has power but doesn't come on then fan motor is bad.

I have a 2004 lincoln ls 3.9 V8 i'm having problem with my new fan it want come on i cant find the coolant fan switch

the fan is a variable speed, don't condemn it until you test the cooling system.

red is from the transmission
check the lines that connect to the radiator for the trans cooloer

Some cars have 2 water temperature sensors with one operating the cooling fan and the other operating dash indicators.

Since your A/C stopped working it sounds like the power may be off in a relay. Want to say go to reputable mechanic so you do not fry your engine.

You also do not want to be taken for an A/C recharge you may not need. Cooling fan should work whether A/C is off or on.

Some fans have 2 speeds so it is possible to need a replacement if only 1 speed works. You need someone to know the power routing. For instance, is the relay getting a signal from the temperature sensor? If the power is going to the relay, does it go to the fan? Is the fan bad on 1 speed or both speeds? This is independent of whether the A/C has a full charge.

Be careful of the spinning cooling fan blades if the fan turns on without warning.

there is a hydralic pump that runs off of the belt that controls motor

poss causes are thermostat stuck closed, replace it, next would be engine electric cooling fan inoperative, test it for proper operation.

there should be a dipstick on the drivers side of the car under the hood to add tranny fluid.it should be red in color