[northern piper]

I'll grant you I've got a 2000 (not 01) but I'm betting the water pump/hose is quite similar. I'd check the junction between the pump and the hose as it's a location that seems to rust. I had exactly what you describe with the drip a the bottom of the passenger side bottom hose. I replaced the clamps (used 2) as they were rusting but really what was happening was the coolant was leaking out of the top of that same hose at the pump and gravity was taking is down to the front by the rad. I'd bet if you look up there you'll find a leak. I won't tell you how horrible that repair is, and on the 2000 the rigid tube is removable from the pump but pretty solidly stuck in there.

Good luck on your hunt!