I was in the process of an alternator install and came across some reading that I found weird. With the battery out I measured the resistance between the hot lead and a good ground, I expected infinite resistance but got ~3.6 ohms.

I found this really weird, is it?

If the resistance is 3.6 ohms and I put the battery back at ~12 volts won't I have a current draw of ~3 amps. I think that would drain the battery pretty quick. With this in mind my buddy and me tried to hunt down where the resistance was coming from. We traced it thought the engine compartment fuse box then all the way into the driver’s side foot well fuse box. Specifically the bottom right 10amp fuse, that says "room". I know this fuse runs the ecu and dimmer dashboard lights, not sure what else. Well we then traced it to one of the white plugs on the back of the fuse box (the one on the bottom right when sitting in the driver’s seat). 5 of the 6 wires coming out of the white connector had continuity with ground and resistance of 1 to 30 ohms. In parallel it adds up to the 3.6 ohms. We tried to follow these 5 wires, but its a mess down there and our wiring diagrams aren't helping that much. I think one goes to the dimmer light, 2 to the hazard switch, can't find the others.

the wires were:
red with black stripe
green with yellow stripe
green with white stripe
green with ??? (can't remember)
white with blue

Is this something I should keep hunting down, or am I missing something?

I know wiring problems are a pain in the butt and appreciate any help you guys could give.
Thanks