“Well, I’ll be a suck egg mule,” Jack Elam famously said in Rio Lobo.
What exactly is such a beast?
A “suck egg” is a young, foolish, or contemptible person, according to Merriam Webster.
A “mule,” when applied to humans, indicates stubbornness.
It’s pretty reasonable to think Mr. Elam was saying he was being a silly stubborn person for not thinking Jennifer O’Neill could be an effective shot.
On the other hand, some think suck-egg mule is a twist on suck-egg dog which are real problems on farms, and are considered to be worse than worthless.
Regardless, the phrase derives from the rural South/Midwest.