Yes you should leave the bilge on ,what kind of question is that ? Also it should be a 3 way bilge ,off ,manual on and auto on. I would not put the boat on a trailer and put water in it . All your doing is introducing water in the hull that may end up reaching some screw holes or who know what that may speed up any possible rotting issues. Of course your trailer may not like the extra 1 -2000 lbs added by the weight of the water. have you used a flashlight and poked around in every nook and cranny while in the water ? That's where I would start