Why is there water leakage between gearbox casing and exhaust shaft seal when flushing?

If the seals are leaking they should be replaced.

remove the drive shaft ( tail shaft) lever out the old seal. put sealer around new seal and fit back in extension housing. Use something that is the same size as the outer edge of the seal and tap it in flush with the edge of the transmission housing. Expect some oil to drain out when the tail shaft and seal is removed

The oil seal is the resistance you feel. take a soft mallet or hammer with a soft drift and gently but firmly tap the stub shaft and it will drive out the oil seal in the hopper direction.The lower skirt of the tapered bearing is what contacts the seal so go slow.
Worked for me.

Hi mate I have no idea what bike your referring to as no information? But most water cooled engines would have two seals to seal the impeller shaft (which circulates the coolant) these seals usually one each side of the inside engine case where impeller goes through one of them holds oil out and the other holds water in hence they called oil and water seals if your sure not head gasket these seals are about the only other way water can get in
I love Yamaha motocross bikes and other MX bikes as they have a specially purpose built hole in the water pump area so when you see it seeping coolant out it tells you straight away needs new oil and water seals
if it is this seal usually only one or the other has gone but no one would replace one with out the other you will see what I mean if you ever replace them as is complete pain just to swap one - you definitely would not want to repeat later to change the other one.
check your impeller shaft also as groves in the shaft is usually why the seal goes in the first place (you may want to replace the shaft whilst you there)
good luck

hi, unfortunatly this is a major job, likely to be expensive, involves engine removal, new gaskets, seals, and output shaft, would check closely first before you buy any parts for damage to the engine cases which may cause oil leakage, or even damage to other internal parts, if you do have crank case damage, i would suggest looking for a secondhand engine, labour bills, new crank cases could make it uneconomical to repaire as they have to match your crankshaft journal dimensions exactly, these would be hard to find secondhand, a used bottom end could be an option

the fluid may be goind out the exhaust, look foe excessive moisture out of the tail pipe, if you gotta fill it so often then its going somewhere right? may be sign of a bad head gasket, jut one more thought, are you using anti freeze or just plain water, water evaps quick, and a bad cap will let pressure escape and evaporate quickly, so you will not see a leak, good luck

Possible causes are seals gone on drive shafts allowing water into the gearbox and thereby pushing oil out of the breather (Oil floats on water )

Or a crack in the gearbox casing

Unplugged water tube, cracked water tube, bad drive shaft hull seal, hole/crack in the hull, cracked water box, broken exhaust jacket water seal, water tubes plugged in incorrectly, no cap on flush kit, broken fitting on motor,etc. Dry out the boat take off the seat and place it in the water and look to see where the water is coming into the hull.

next time you start it have a sniff of you exhaust if it smell sweet like coolant then you have an head gasket gone

Here is a website where a manual for you outboard may be purchased.  Outboard Marine went out of buisness in 2000 and thus no parts of origial manufacture are support is available . Therir are secondary markets .    THe Lower case splits in half and their is a seal around the prop shiftm which is pressed in. The seal between the cases are cut o-rings which are placed and glued into place with gasket seal.
The water pump is located where the case splits a little bit higher. You must open the little port on the side and take out one of the screws to the connecting shift linkage to split the case. After splitting the case the drive shaft and water pickup tube(s) wil come out of the powwer head or the tubs may stick into the power head which is ok. Place the lower skag into a vice and remove the 4 or 5 screws to the water pump housing. Remove and replace impellor and impellor plate if available. If part(pieces) of the rubber impellor is missing flush out the tubes and the power head to remove them.   When reinstalling the lower unit use a flash light to make sure that the tubes return  to the proper place in the power head and the shift lever is resecured. If you need more assistance, just write back. I was an Outboard motor mechanic for five years about the time of your motor.