I don't rinse after use ..I cleaned the entire unit a few years ago..waxed and it came out A OK..The heat from the upper gear box crystallizes the various minerals in the muddy Oklahoma lake water..creating a whitish film..which is very hard to remove..Zinc are in great shape...there is a upper lower unit shower that is sold on line...that sprays water on the upper unit gear box to cool and according to the sales pitch on line keeps the surface finish looking new..
.IMO..it all comes down to the temp of the gear box..the hotter the ambient temp, lake water temp and amount of use...the minerals or water chemicals are going to adhere and discolor the OEM surface ..
I've had very good results with Star Brite Premium Marine Polish With PTEF . Clean it thoroughly, and polish and wax with the Star Brite. In 2 to 4 weeks, give it another coat. Then in another 3 - 4 weeks a third coat. The polymers in that wax will form a very smooth surface that does not allow anything to stick to it. Surface will then be very easy to clean with soap and water, or if its really scummy, a mild marine scum remover.