The speaker or beeper (probably in the handlebar cover) on Sea Doo's fail over time or work intermittently.
I own 3 Sea Doo's ('96 GSX, '96 GTi & '98 SPX) and the beepers all work whenever they want to. If I plug the key onto any of the three's DESS post. It's always a toss up if it beeps or not. But as long as the gauges & lights light up on the handlebars and it starts. I'm on the gas and gone!
But here are a few more questions for you since we don't know the history of this ski:
1.) Is the paint on the head bolts in tact or are there some pieces of paint missing? This would tell if the bolts have been removed or tampered with in some way. I'll attach a picture of my '96 GTi's head bolts for an example.
2.) Have you checked the clearance between the rotary valve cover and the rotary valve surface with a feeler gauge?
There is a spec in the manual that needs to be checked.
Just some food for thought...I was thinking that if the engine was rebuilt that the rotary valve timing might have been set incorrectly or that the rotary valve shaft's brass gear might be damaged. You would need a timing wheel($15) to set it correctly.
But since it hasn't been rebuilt. I wouldn't totally rule that out.
The rotary valve can skip a tooth on the shaft gear and also throw timing off.
The rotary valve shaft has a brass gear on it(41 teeth) that is meshed with the crankshaft and as the crankshaft turns. It turns the brass gear which in turn turns the rotary valve shaft which turns the rotary valve underneath the rotary valve cover which covers one intake opening where one carb sits above it and the other intake passage is left uncovered for the intake of air, oil from the injection spigot as the carb butterfly is opened by the throttle cable from the thumb throttle.