that could simply be moisture due to lack of oil change for x years or it could be leaking.
to do a pressure test buy a gearbox oil kit, it will come with a screw hose which you can attach a pump to somehow and put some pressure on it. i must admit i do not know what that pressure should be so someone else will need to answer that one.
as for your makeshift shaft test with a screwdriver, certainly a good start! that only proves not massively out though, we are looking for very small differences here. (i think 0.03 inch is the max recommended for mercury, i don't know about suzuki but i would imagine they are all similar as it is a spinning part after all)...check this out.
another one- (this guy heats up the shaft but need to be careful as that alone could kill the seals, TBH i wouldn't put heat on it as you couldn't get it hot enough to make any difference and keep the seals good, although i have never done this so happy to be wrong?)
And the leak test, you should also ideally pull a vacum too.