If this is the case, how urgently do I need to change the stator, considering I've probably been riding with it for some time?
Couple things, it appears only one pole is shorted, years ago , sometimes a partial rewind was done, you have 18 poles, if only one is trouble, you could rewind that pole and put it back in service.
Invader looked close enough to notice, and he is right as to this has been going on for some time. The cover needs to be replaced, the stator is held precisely over the rotor, you are taking a huge risk trying to repair the cover, all you need is for the rotor catch the stator, dislodge some fragment of metal and get it in your motor.
As to running as is, you could remove the winding of that pole and jumper the connection, that pole is acting as a load if it is shorted.
There are numerous pictures of stators on this forum, including a Y connected stator, looking closely at OEM and comparing to a Y connected stator, the Y has less copper, so the space between poles and windings is greater. Also somewhere between poles is a connection of 3 wires.
The difference is comparable to running a electric lawnmower on a 16 gauge cord or on a 12 gauge. The 16 will run hot and the lawnmower will have no power, having said that------some lawnmowers were designed for 90 VAC , taking into consideration that the cord used may not be heavy enough. There were warnings on those mowers to not use less than a 50 foot cord.
Back to your question of continued use, your bike your choice, eventually you will have a dead battery and be without a ride if your stator fails completely.
If you follow this thread http://www.kawasakiversys.com/forums...tml#post951489
I have some tests on page 2 and 3, that could be done to prove what is going on.