Car is shut off, switch is verified as off, key out of ignition. Fan for blower (heater / air conditioner) stays on. Also, When car is on, fan blower adjustment for speed does nothing. Back to car off, even removing fuses in the car, AND fuses and relays under the hood, would not shut off the fan

i will now read the online service manual to you.
https://eautorepair.net/Marketing/Default.asp

blower fan located where. dash heater blower fails
or radiator fans of some odd kind added later.
coolant fan or dash? there are 2 coolant fans and 3 relays to run them and all 3 relays, can fail and coolant fans blow for ever and ever. fuse 6 kills the relay coils. only, so if relay is welded fans blow endlessly. even if bcm is removed from the car.
on the other and the heater blower is 100% controlled by the BCM

so car engine starts and runs and drives ok right.
when did car last run perfectly> , or seen ever ?
service manuals for 88 cars are not easy to find
means real oem manuals, best. 35 years old !
no digital then ,just a huge paper bound book, remember?
holy moly this 88' has a body controller here, bcm , relic amazing thing.
facts: 1988
here is proof

The Mercury Mystique had somewhat of a bad reputation for wiring problems. I guess my question to you is have you had to have the wiring worked on?? If so, I'd guess that it would be pretty possible for a wire to be hooked up wrong at the ignition switch if somebody has been fooling with that. Just a thought... Also, I'm wondering if the fan continues to run until your battery goes dead?? Now, I'm hoping you don't have the blower motor (for the heater and air conditioner) confused with the electric engine cooling fan. It is normal for the engine fan to run for a while after you shut your engine off. But, I'm probably telling you things you already know along that line.

Depending which HVAC system you have Manual (sliders for temperature) or Auto (digital readout), the control module is likely at fault. The Manual HVAC has a Resistor Module (which have a high failure rate) and the Auto HVAC uses an electronic module. Both of these are mounted next to the blower motor located behind the glovebox.

OK, if the relay for the A/C fan is bad, then the radiator's fan will keep running after turning off the ignition. Also, if the fan for ventilation of the A/C in the cabin stays on after the ignition is turned off, the relay for that is bad.

Good luck on this repair.

You have a short in the switch or resistor pack. replace the switch

are you talking about the fan blower inside the car or the fans under the bonnet..? the fans under the bonnet may stay on for a while after the engine is switched off to prevent heatsoak. This is when the engine actually heats up more after switch off due to latent heat within the engine. The fans will remain on until the coolant temperature has fallen and stabilised, then the fans will stop. If the blower fan inside the car keeps running, this may be a feature on the car to assist with heat soak but I would think this is more like a faulty power relay or fan controller if the car has climate control..In this case, my advice would be to consult a qualified autoelectrician.

check fuses,could be fan switch or at worst fan motor,need to get it looked at,

Should have a blower control unit. Sometinmes these are known to leave the blower running on low speed with the key off.

Either you have connected your wiring incorrectly, recheck all of your wiring connections, Or the power supply for the fan is coming straight from the battery instead of running through the switched relay, most likely the relay is stuck closed allowing the fan to stay on.

If the heater blower motor resistor failed then the heater will stay on full blast to keep your window clear, for safety. If the key is turned off and the fan still blows then I suspect you have an ignition switch problem. Main power comes from the key switch to feed the heater system. The plug at the ignition switch could be melted and making contact or an internal switch problem. The switch is located on the steering column under the plastic cover.Unplubbing the switch should help diagnos the problem.