Sounds like it could be a simple wiring or ground issue. I would start with this. When you insert the lanyard the gauges (spedo and tach)should spike up from full to zero once before the boat starts. If your tach is stuck on 4000 regardless of lanyard on/off or boat started/not started then it is not getting power or something electrical. Have you checked to see if it illuminates at night with the navigation lights on? Do you have any issues with any of the other gauges?
First check all your fuses. Next, with a multimeter check the ground. You may need to remove the wires on the back of the tack and clean them if they look corroded. If your ground checks out good then look at the power, does the gauge main power wire get a spike when you insert the lanyard and/or when it is running. Need to determine if the gauge itself is dead or if there is some other problem further up the electrical line, such as not getting a signal from the computer. It's all voltage, nothing particularly complicated.
I have had trouble with my tach before, and it turned out to be electrical in nature. Sometimes it runs about 1000 rpm too much, and if I tap the gauge with my finger it goes back to normal. Next year i plan to clean all the electrical connections at the back of the gauge very good in hopes of solving my problem.
Since you have the analog gauges, I don't think taking it out will cause any operating problems. I also suspect you can probably replace it with an aftermarket gauge, but do not know for sure; the Seadoo OEM gauge is at least $300.
Electrical gremlins are a real pain but hopefully it is something simple. Good luck and let us know how things turn out!