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If the 2007 350 is the same as my 2006 342 in this regard, you will find the sump box on the port side under the mid berth mattress on that side of the boat. If you remove all the mattress pads, you should fine several interesting hatches that lead you to the forward bilge sump pump, the AC inlet valve and hopefully the shower sump..
You will recognize it. It is a covered white box. When you remove the cover you will see the float activated pump and the little storage compartment that fills with the first incoming water. Your shower uses a sump because the shower floor is below the outside water level.
Salt Shaker 342
IF its similar to the 360 my sump is at the bottom of the stairs. There is a large storage hatch in the floor which has the AC thru hull and strainer in it. In the rear of the hatch pretty much mounted flush to the underside of the cabin floor is the white sump box. Its a pain in the butt to access because you have to drop the box off its brackets to do any service on it.
I have a slow draining shower and i think its actually the waste pipe that is somewhat clogged. The pump works fine its just the sump isn't filling up fast. If you can rule out the pump that woudl be a good thing. Good luck.
Had to replace mine on my 2000 340 FV. This is the one I bought. Looked very similiar to the one I took out. It was located under the mid berth.
2000 340 FV