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Can you hear the fuel pump run for a few seconds when first installing the lanyard?
As you know the problem is usually caused by leaking o rings on the oil cooler in the front cover. If the o rings are good then closely inspect the cooler for a crack. I have seen this a couple of times.
There would have to be an awful lot of water inside the hull for it to draw water into the intake. If the model you have uses the paper air filter mounted in the front of the engine then that would be more likely. In that case check all of the clamps on the rubber hose connections for the plastic air tube. That tube also has a water drain on the bottom of it with a clear plastic hose that ends near the driveshaft. Check the hose is secure on the tube and that the plug on the end of the hose is in place. It would also be a good idea to check the strainer on the end of the suction hose under the driveshaft coupler to verify that it is not clogged with trash.
The f12x uses a high mounted air box at the rear of the engine. Here is a link to a parts diagram:
This design is much less likely to get water into the intake. Also, if there was water being drawn into the intake then you should have seen it on the sparkplugs and it should have shot out of the sparkplug holes when you cranked the engine to check for spark.
So, if the water is not coming from the air intake then the oil cooler is the most likely source of the problem.
I do not have any other suggestions for you. I will opt out.