Look it this way.

It is entirely possible that some singer, singing "Riding on a Donkey" on shipboard in, I don't know, 1893, thought "Hmmm...I wonder if this has something to do with the donkey engine.....Yes, the more I think about it, the more sure I am. But what? Huh!"

So what?

It would only be significant if we knew that "riding on a donkey" was a phrase actually used to mean "operating or employing a donkey engine."

There is no seafaring evidence that the phrase was *ever* used that way.

No memoirs, no collectors, no Stan Hugill. The only evidence we have is an assertion in a children's book in the 1930s, plus further assertions by landlubbers decades and decades years later.

Watch this: I claim that "riding on a donkey" meant "on shore leave." How do I know? Because I do. Now prove me wrong.