I had/have a similar issue, as Mallo does, on a 97 gp 1200. With this one it seems that the relay stuck and it toasted the starter motor. When I touched the - cable to the battery it would spark. So I chased it down to the relay. How in the heck do I get the starter off of this thing? I have a service manual but it doesn't give much info on removing the starter. Does the exhaust pipe/muffler have to come off? As near as I can tell the starter is underneath there. Thanks!
Check your starter as I had similar on a Kawasaki when the starter solenoid had gotten stuck.
I would take the starter out and give it a good clean and spray it with a good electrical Marine spray.
the problem is that the Starters are normally in a hard to get spot when spraying the Ski after a day out on Salt water.
I like to fill my hull with fresh clean water and a good quality salt remover and then spray with INOX after I drain.
I only fill to a level that it flushes the engine mounts and starter as well as any clamps in the lower section you may not easily see.
I found I was having to many problems with my two old Two strokes and sold them both and got a newer Four stroke and haven't looked back since.
I now use less than half the fuel and even though the servicing isn't the cheapest, as it costs me $300 for a proper Yamaha service.
The saving in fuel makes up for that
Lucky the starters are not an expensive item for that Ski, good luck and hope that fixes your problem.