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If what you are calling the "pee hole" is the round vent at the back of the engine, this is the idle relief vent. When the engine is sitting low in the water--like at idle-- backpressure builds and exhaust would normally be refluxed into the ports and cylinders. The idle relief vent reduces this backpressure by venting exhaust out the hole. The engine will be less likely to stall and will idle better.
TYPICALLY when running, water is passed through the block and head then exits into the leg along with the exhaust. On muffs or during idle, water and exhaust will spit out the idle relief vent. At higher speeds, the leg fills with water and a steady stream will or should exit the hole along with some exiting the exhaust snout. Exhaust will preferentially exit the snout which is now much higher in the water. The water pump itself should not cause any bubbling. However, you should recheck to be certain the water pump is not ingesting air.
Look closely at the attached photo and you will see the stream of water exiting at speed.
Depending upon the engine and idle speed, at idle, there may always be exhaust venting through the snout, bubbling under water.
If you are absolutely sure this is a new occurrence, remove the six screws holding the two halves of the shroud and remove the shroud. The idle relief vent cover is held to the leg with two screws--do not destroy the cork gasket under it. In the leg behind the vent cover held with the two screws you will find two holes. Probe the holes to see if they are clogged.
BTW: If you ever need to remove the powerhead, there is a bolt hidden under the idle relief vent cover.