The fan can be fused full time power but the relay that is controlled by temp and AC should be key on power, or fan would continue running after you parked the car/truck until heat was below temp threshold
Some vehicles had that setup, but usually had a timer with it so it could only run a few minutes after key off
Or there would be a dead battery in their future, lol
And never understand that thinking, when engine/key is off, there is NO coolant circulation, so cooling the rad coolant with the fan doesn't do much for the engine, lol
I guess maybe the fan in the engine bay would circulate some air, but it would be hot air after coming thru radiator, no, I never did see the benefit of that
I ran my first setup straight to the battery. Depending on the outside temp, it would cycle on and off after I turned the key off. It never ran the battery down and it seemed to help heat soak on the carb a little bit, that may have been my imagination. It did cycle on and off, so that tells me it did have some circulation in the coolant with the engine off. I had the probe inserted in the coolant loop to the heater core.
I transferred this setup to the 2.8 Bronco II I have now, and during the hottest weather climbing the mountain everyday, it would get up to 230 on the temp gauge. So I swapped back to the mechanical fan and it kept it cool, not getting over about 215 on the worst days. But the mechanical fan was noisey and put a lot of load on the engine. When you only have about 100 hp, taking anything away from that is noticeable.
I started looking for a better electric fan for cheap. I found a 2 speed Taurus fan at the local junkyard for $35. A little cutting and trimming and it fit. I had done some experimenting, the aftermarket 16 inch fan I had pulled about 10-12 amps. I checked the Taurus fan on low speed, it was pretty lazy and only pulled 8 amps. I knew that would not be enough. I tried high speed, but my meter only went to 15 amps and it blew the fuse in it. When I touched the high speed wire to the battery, it made a pretty good spark initially. I was afraid it would ruin my cheap full voltage thermostat I was using, so I did add a relay to handle the extra current. I used the power from the emissions vent solenoid on the carb to power the thermostat and relay for the control power.
So I am using high speed only on the Taurus fan. I works very well so far. I have it set to come on at about 215. The engine has a lot more pep now it's not turning the mechanical fan all the time. I was worried about the stock alternator turning the Taurus fan at high speed, but it does fine. And with the relay it does cut off now when I turn the key off. I went ahead and took the A/C system off, so that extra bit is not needed on mine for now.