I have a 1988 350 Mag with an Alpha one. Water is coming into the bilge with the trim all the way up. My mechanic says all the boots are good. You can see the water streaming down the back of the transom cut out.
What did the mechanic do when you showed him the water? He didn't investigate further.
Chances are good your transom seal is gone or the upper swivel shaft seal is gone. These are big 0-rings (basically). You can buy replacements through your dealer. You can try socking down the mounting bolts tighter to compress the seals but....
Given that the boat is a 1988, you might have a soft transom.
The transom is plywood cored and after 20-something years water can start to rot it. If it gets soft, no seal is going to work.
So, first pull the mounting bolts and examine the core of the transom. Is it dark and mushy or clean and firm. If the latter, replace the seals. If the former, you need to get the transom re-done ( This can be a DIY affair, provided you are handy with a grinder and fiberglass)