radiator fan used to stop as soon as the engine stops?

Hello,

It sounds like you might have a faulty radiator cooling fan control module.
As the module is basically telling the ECU that the engine is too hot and the fan keeps running.
This was a common issue among these lancers. There was even a recall to change those modules out.
This was a common issue with the Lancers that were in a humid climate, as moisture would make the circuit board on the module for bad.

The fan control module is located right behind the fan (see diagram).
There is a quick way to test the module. I have attached the testing instructions.

https://www.2carpros.com/articles/how-an-electric-cooling-fan-works

I have attached diagrams for your reference.

Please let me know of any questions.

Thank you.