A family of phrases/ suggestion

The pattern that interests me is:

"Let us make like a [noun] and [verb]"

Usually, the phrase arises on the occasion of departure or transition. There are many clever variants, such as

"Let us make like a bakery truck and haul our buns."

The question is: what is the original phrase, of which all the others are imitations? From whence did it originate?

"Why don't you make like a tree and leave?" must be an early ancestor of this group.

This isn't a construction that's common in England. Is its origin in another language?

I have a book with types of phrases. I'll have a look.

I entered "make like a *" into google and was presented with 32,000 pages. I looked at a bunch and they were all from within the US of A.

The strangest:
Lets make like a fetus and head out.

"Make like a tree and leave" is a punning U.S. insult, heard among schoolchildren and probably others.

Phrase Finder should compile a list if similar common sayings for easy reference in the archives. I was unaware that "make like a tree and leave" was an insult. I have only heard these used in a humorous way.

Others include:
make like horses*** and hit the trail!
make like a hockey player and get the puck out of here!
make like a whale and blow!
Any other suggastions or examples?