Finding serial no. on a 90 hp from the eigties

Hi all!

This is my first post here, I suspect it won't be the last.

I recently bought my first boat and it has an old 90 hp two-stroke Yamaha on it. I suspect the year is 84-86, but I don't know. The reason I don't know is that the plate with the serial no. is missing, which is a problem for several reasons.

Is there any other way of finding the serial no. or am I bust?

[boats.net]

Sometimes the serial number will be on a aluminum welch plug on engine block.