Just unplug it. On the beeps, test the beeper by unplugging it under the steering and send 12 volts directly to it. It should 'beep'. You need a good beeper to figure out what's going on, since that double beep is an indicator everything is a go at the MPEM to start and run. Yes, there should be a small gauge negative wire at the battery along with the starter to battery negative wire.
TL/DR-Quick answer, 1997 GSX's changed various parts and wiring mid year, so the ground is gone, the VTS & MPEM are NOT the same units, MPEM replacement doesn't look good. None of the repair sites appear to service the new one piece model. Use caution at a dealer, if one that fits is offered many don't work on 2-strokes. The buzzer test is a great idea! I'm wondering if it's a symptom or coincidence, this can help answer that.
I'm almost positive at this point that you're thinking of a different ski, at least for part of it. Honestly if I hadn't spent hours searching various threads and piecing them together I'm not sure if I would ever have realized it until I started trying to replace something. Apparently in 1997 SeaDoo updated at least the GSX, maybe a couple others as well but I don't have them to poke around, and the specific model has a serial numbers you can get an idea of when it was assembled. Some changes are available on slightly older ones, like it appears the VTS unit was changed from 96 early in the build model, but later in the run the MPEM changed, the second wire (believe me, I searched for 2 days because it's a perfect fit) doesn't exist anymore, and things like the electrical box wiring changed a bit. I only have 4 grounds at the lug where many report 5. There's a few other odds and ends to trip people up. I also have a different model 1 year older and part of my search for that ground was remembering seeing a smaller gauge wire connected on a battery but I'm pretty much positive its the one on the older ski. Man, I really was sure that was the answer, by the time I moved on my dad got curious being retired from a 40+year electrical career as well and after I described the issues told me I had obviously buried a ground behind the new battery when I put it in. A few hours later when I checked on him he'd put the battery back and moved on to the VTS. It's odd because it's never worked but now it's the only place power is found after it leaves the electrical box to go forward. I'm going to test out the assorted positive leads at the MPEM tomorrow to try to figure out exactly how it's distributed and controlled at that point. I am wondering though, with a ground issue being such a good fit, what about the MPEM circuit? It's (+) is fed ahead of everything else from the source it seems, and the (-) appears to be at the plug on the stator cover? I just saw it mentioned earlier and I'm at the point of tracing out every system and drawing up a ladder diagram. I'm thinking about getting a buzzer, maybe pull the other skis and use it to test, but something I noticed in other threads is either the damn thing dies exactly the same time as another thing and it's just coincidence to a point, but the other one is it stops working along with the ignition and the other critical systems. So is it another symptom, another odd coincidence, or just these things at some point shake themselves apart in one big pile like a shithouse shack in a good breeze? But yeah, rereading your comment to make sure I didn't miss anything and I had of course. That buzzer test is first thing tomorrow. Sorry about the wall, but if someone had posted this over the years it could've saved me a lot of confusion and trouble not to mention at least a good chunk of hours. I haven't played with advanced test yet, tried to before bed tonight but I didn't get the sequence right from memory and I'll try it tomorrow, maybe get some beeps like a few other guys with similar issues did. The worst part though, if you look up repaired MPEM modules most of the guys have a cut off year that's 1997. Sweet! But no. It has to be a 1996 model 97, the 1998 model 97 has that combined unit that can't be converted to a standardized one because of the 27-pin connectors up front without a complete rewire.