Here are the steps I take when running any ski boat on a trailer:
1) Elevate tongue near max. (hull drains better)
2) Open or remove motor box and or rear center floors (I am typically doing alignments etc. at this time & prefer to really open up the work area)
3) Place a 5 gal. bucket near the water intake area, disconnect the most convenient suction hose & redirect it -or- add a section of hose into the bucket.
(I have a piece of corregated plastic swimming pool suction hose that resists collapsing that I use with the end that goes into the bucket cut at an
angle so it resists sucking to the bottom)
4) Fill the bucket to within an inch or so from the top with the suction hose in the bucket - shut off the supply hose
5) Squirt the shaft strut under the boat with the hose (I use a spray bottle with 10% soap)
6) Start engine & immediately watch the water level in the bucket, if the water is not visibly going down within 5 seconds, shut off the engine &
carefully feel the raw water pump, if warm to hot correct pump problems, if cool restart & try again, if still not drawing water, after another 5 sec.
correct pump problems.
7) I usually turn the hose/water supply on as the bucket draws down to the half way mark

NOTE: A typical ski boat will consume water fast! depending on hose size, city water pressures & idle RPM, EXPECT 600-1000 RPM to consume water as fast your hose can supply it!
9) I usually need to shut the engine off within a couple minutes to allow the bucket to refill since cold engines idle higher, while re-filling check the oil
dipstick for oil that is clear, if turning milky, your winterization program failed, shut the project down & have a drink.
10) Always let the engine pump draw water as needed, never allow it suck air, never force water into the system.