This is the one you want, this particular one is a bit high by a few bucks but it has the same waterproof connector on it so those cost a few dollars more then the basic $20 solenoid.
Money well spent though, to avoid tearing up your starter, and these things do tend to stick. Again, you need to check out your starter button too, it might be binding as well. Why risk it though? The reason I think the solenoid is sticking is b/c the idle speed was not acting right and it's very common for the solenoid to stick, it's very similar to many other marine types and I probably find 10 or more that either are burned, don't make contact, or tend to stick.
This device shuts on and off, the power to your electric starter.
http://www.ebay.com/itm/SeaDoo-Star..._Accessories_Gear&hash=item4ad35c072c&vxp=mtr
So just follow the big fat cable that leads from your starter and you'll find it leads to this solenoid. Before changine it, disconnect your negative battery cable from the battery. There are two nuts on top threaded onto the studs, remove them and the cables that connect to the studs. Then you'll see an electrical connector attached to the side of the solenoid, it has a little latching lever on it, slip a small flat screwdriver under that, or maybe your finger nail and lift the latching lever (try not to break it off) and pull the connector off the solenoid.
Reverse the process to install, be careful not to torque the two nuts too much b/c the studs are copper and can strip the threads, they must not be lose though or they won't carry the high current.