Been awhile. I non longer have my 2002 90 nor my service manual. To answer your question about an Over Rev. Module problem. Sounds like you are on the right track with a OR module problem. Mine was the same engine with some upgrades. Some engines came with it in the series and some didn't. Mine didn't have the module. As I remember from the manual wiring harnesses, those with it had a module and I'm guessing it's about 1 to 1 ½" square, epoxy construction. Giveaway would be the wiring.
To get the signal to cut back the rpms, the TACH output of the rectifier regulator module, Grey wire on mine, would have to go to it and then off to the electrical connector that connects to the remote cabling sending the signal off to the tach in the boat. In addition to that would be power, Red, and ground, Black, trigger input from stator, color I don't remember, and a signal wire over to your triggers in your CDIs or switch box (if the '96 had that) which has all the CDIs in one place rather than individual modules like mine.
The triggering system was off the single stator coil and there were 3 magnets on the flywheel. In addition to that, but not related were the 6 coils for the Red battery charging stator under the flywheel but not related....that output was a pair of yellow wires.
The single system trigger coil, under the flywheel, sent out a trigger every time a magnet passed which was 3 per rev, 120 degrees apart. That signal was daisy chained through the CDIs and each got hit 3 times per rev but only one was setup on a cylinder that was ready to be fired so it was a "wasted" hit for the other two. So coming out from under the flywheel you have 2 sets of wires, one for triggers and one for battery charging.
Don't remember the wiring but I think the trigger went to the "Over Rev. Module" where by it was passed on to the triggers if ok or shorted out internally and not sent to the CDIs if too fast. I'd imagine that it would take in the lot but only let a reduced amount out. That seems to coincide with your comment about how your rpms are acting. I do not remember the color of the signal wires from the stator but you only had signal and yellow battery charging pairs.
I'd follow the wires I mentioned and when you find the module you possibly can just unplug it. If the trigger wire from the stator is jumpered to another wire going to the CDIs, at the connector, then this will/should work. Otherwise: Merc made several harnesses to suit the occasion and the manual listed these...had to select the one that applied to your engine.
The only problem with what I said about unplugging it was that if the trigger comes in one pin (of the module) to be processed internally, and then out another pit to go to the CDIs to trigger them, you'd have to jumper those two wires together at the connector when you unplug it.....which isn't a big deal, to get the signal from the stator to continue on to the CDIs....wiithout going through the OR module. Just pay attention to the color codes and select the two wires at the OR module connector other than power, ground, and tach input as mentioned above and short them together with a jumper which would route the full compliment of triggers to the CDIs with no cancellations.
The engine has no oil supply sensor. The Over temp sensor is as Silvertip said and can be removed from the circuit by following that tan wire he mentioned from the sensor, located on the top left rear of the engine block water jacket cover over to the wiring harness where it is connected...just unplug it if concerned while troubleshooting.
Best I can do.