The thing I don't like about it is when working under the hood; I'd always be paranoid that the fan might start up on it's own.

I was thinking about that too. However, I'm happy to report that I've corrected the issue. There is in fact no timer on this control. It states in the instructions that you are to connect it to an ignition source that is on when the key is on, or if you want the fan to run while the vehicle is off then connect it to an always hot source, which is what I'd done by mistake. So, I bit the bullet and changed the wiring. Actually, the whole thing only took about 15 minutes... ended up tapping into the starter relay (used a test light to verify that the pin I was splicing into was hot only with the key on). Works exactly like I'd expect now.