Hey brah.
I might not be following (happens more than I care to admit).
Remember, an item only draws what power it needs. For example, you could hook your fan up to a 15 amp circuit or directly to the battery and it will draw the same amount of power (it's like a horse drinking from a large trough or a lake. The horse doesnt drink 100 times more water or drink it faster because the body of water is a lake).
If your fan has a rated spec of 10.5 amps, do you know if that's continuous draw? Some fans can have a start-up draw of 100-300 times their rated-continuous draw (and on the flipside, they become generators when powered-off but still spinning).
In any case Frank, consider using a relay if you want. You can then choose any power source you desire. The chosen power source (i.e., the cigar lighter) will turn the relay on (the draw of turning on a SPDT/SPST relay is about 1/4 amp). Then the fused battery power to your relay will power the device itself.
Alternatively, if this fan will not be used when the HVAC fan is on, that's a 30 amp circuit which could be used. Note that it is only hot with the key on however.
If I totally missed the boat, post up and I'll get it right.
Good luck with the project.
