Justin, the float switch should be in the same compartment as is the pump itself, for a whole host of good reasons, not the least of which is to avoid the confusion you experienced when first not seeing both at the same time. The pump should never be told from a remote location to pump where it (the pump) is now. Any mismatch in levels between the two places, or an even slight out-of-trim condition could fool one or the other.
I'd recommend a Water Witch type (WM sells one) which has two electrical contacts in a small sealed rectangle. When the two contacts arc through contact with water, the pump goes on-- no moving parts and nothing to jam it, clog it, fool it. These can be had for about 30.00. Word to the wise-- carry a spare one. Like anything digital (on-or-off), when it goes it goes and that's it. The flapper types can usually be prodded into more work. Luckily, changing a Water Witch type is as easy as unplugging two wires and plugging them back in.
Consider making a 'permanent' mount for the pump and switch, into which you can just plug a replacement pump. I cut the little blue basket for my Rule one (to make it fit deeper) and mounted it into the bilge; for a replacement pump I can just snap the new one into the old one's basket.
Another word to the wise-- cheap bilge pumps seem made for West Marine's extended warranty. When I worked there I called it a 'subscription to bilge pumps'. Pay 8.00 for the warranty, and every 2 years, no matter what, return the used pump for a new one and buy a new warranty. That's it. These things WILL go; make that work for you.
Also, Justin, avoid that cheap corrugated plastic hose. At Cherubini we used that only for the initial run from the bilge pump out of the bilge sump; this was to allow us to pull the pump up 32" from the depths to work on it. After there we used the heavy-duty sanitation hose, which is approved for seawater. Remember the bilge-pump hose does two vital things: it removes water from the boat, so you have to question why you have to do that (boat is leaking or sinking); and it prohibits its own contents, including that which may find its way in from overboard, from leaking into the boat somewhere else. For this you need good hose. That cheap corrugated stuff belongs on children's science-fair projects and in hipster art studios-- NOT on your boat.