There are some people who wire up the auto side of a pump to a switch. In my mind that defeats the whole purpose which I think is what you're saying too. My auto pumps are both wired direct to the batteries (one each) and cannot be 'turned off' because in my mind, an auto pump should be just that - something that can automatically take care of water even when you're not using the boat. Just make sure to have an inline fuse near the battery. I used the posts on the back of the battery switch for these connections.
The purpose of the 'manual' wire is to allow you to get rid of nuisance water that isn't high enough to cause the auto switch to go on and also in case the auto switch fails.
From your description, it sounds like you have the Rule-Mate 500.
Assuming you want the automatic feature available all the time, you would wire as follows: The solid brown wire goes to the automatic side of the pump. As such, it should be directly connected to 12V. The brown with white stripe is the manual switched power and should go to a fused switch - then to 12V. Black goes to gnd.
The fuse spec for this pump is 2.5 amps. As such, your 10ga wire is way overkill. It won't hurt anything if you happen to have it laying around, but 14ga is plenty, even for that run.
You may also want to refer to my schematic which shows how I wired my pumps.
https://fishyfish.com/boards/index.php?topic=93.15 Ken
