I would think that seals would be a suspect, however, I am new to jet skis, so I don't know for sure what all the possibilities are but I am good a troubleshooting and I know how I would approach it.
I would put it in shallow, weed free, water about 2 feet deep, remove the seat, and wait for a while to see if water is getting in when it's not running. You might need a step stool to get high enough to see all the way to the bottom of the engine compartment with it in the water (I know I would). If no water gets in, then I would tie it off using the rear tie downs tied to an anchor (the kind with an auger blade that screws 3ft down into the lake bed) and then start it up and see if water is getting in while it is idling. If I saw no water getting in that way, then I might throttle it a little bit, just above an idle, because in only 2 feet of water I wouldn't want to risk sucking something in. You might need someone else to throttle it while you look for water getting into the engine compartment. Even if I couldn't find weed free water to run it in, I would still at least look at it with it just floating in the water.
I would hope to see exactly where the water was getting in and then go from there. If I couldn't see the leak, or I couldn't find a suitable water location to do the run testing, I would call around for a service shop with a test tank, find out what their labor rate is, and maybe pay them to look at it for an hour under various throttle conditions all the way up to full throttle. Maybe they can identify the leak.