[ImperialCrown]

There are high and low speed fan relays in the underhood fuse/relay center. They are turned on and off by the PCM.
For some reason a relay may be shorted on or the PCM is getting wrong information about engine temperature or if the A/C-defrost is on or the PCM itself may have an issue. Any 'ck eng' light on or fault codes?

 

[ImperialCrown]

Yes and their locations (high speed relay and low speed relay) should be labeled under the lid or next to the relay itself.

 

[ImperialCrown]

It could if it was a signal value out of the high/low range that the PCM allows, like an open circuit or short to ground. If it is still within a 'believable' or valid temperature value to the PCM, it shouldn't set the 'ck eng' light.
If a rad fan relay is pulled out with the ign on, it may set a code as the PCM sees an open circuit to the relay actuator coil.

 

[ImperialCrown]

Both fans do run in the low or high speed mode. They are 2-speed fan motors.
If you pull a relay and the fans stop, that is the circuit (low or high speed) that is staying on.

 

[ImperialCrown]

For diagnostic purposes, it would be OK to swap the 2 relays with a couple of 'non-critical' adjacent relays of the same part number in the fuse/relay center.