Warning lamps when fan comes on

That source might have used a isolated ground in it's circuit. Nissan did some weird floating grounds with some stuff in these cars.
It's usually a sound idea to run your own wires for aftermarket accessories unless you understand the circuits you are tapping into.

If you use a thermostatic switch with your relay, you don't necessarily need a switched source. I use a fused wire right from the battery terminal
as the thermostatic switch will control the fan. They suggest you use a switched source, but I've personally not had any problems with the taurus fan
running very long past when the engine shuts down. I have the temp probe tucked into the radiator fins at the top of the radiator near the hose fitting.

If i did have to locate a switched 12V signal i trusted, i would use the one from the cigarette lighter and route it to the relay.

Thank you Z_Karma. I wired it to the battery as you advised, and you're right- it doesn't run very long after shutting down the engine. I was concerned it would drain the battery but I don't think it will be an issue. If I get a wild hair one day, maybe I'll connect the switched power from the lighter. Thanks again!!

I imagine the direction to put it on a switched circuit is for safety reasons so that you have a method of securing the fan off when you are working around it. I would recommend pulling the fuse for the fan in those situations "just in case". Just remember to put it back when you're done.