Sounds like the battery vent hose. The original battery was a flooded Yuasa battery that had a vent that connected to that hose. That way if the battery was shorted it would allow the acid to vent through the hose instead of inside the ski. By now you have probably replaced the original battery............hopefully with an AGM maintanance free type that does not need to be vented.
The vented battery was never a good idea. My original battery vented and ruined the decals around the back of the ski when acid came out of that hose under the rear seat. I'm lucky the paint was not damaged. If you still have a vented type of battery, you can hook that hose to the vent, which will be a little plastic tube coming off the top of the battery. Or better yet get rid of the vented (flooded) type of battery and buy an AGM and don't worry about the hose.
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2008 Yamaha FX HO Cruiser
2010 Hurricane Sundeck 2100
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