Swearing by the Gemini was a mild oath back in classical Roman days.* They were the equivalent of euphemisms, like saying “Darn” instead of “damn”, and were thought of as curses used by women.
There is speculation that the similarly mild expression “Jiminy” is really a corruption of “Gemini” (Not that the use of the older sayings survived 19 centuries. If this is true, I suspect it’s a use that trickled down from Classics professors and the like reviving the practice).
Furthermore, the form “Jiminy Cricket(s)”, which long predates Disney’s Pinocchio (look it up on Google Ngram), is probably a transformation that makes the expression a euphemism for “Jesus Christ”, along the lines of “Judas Priest” or “Cheese on Rice” or “(Great) Ceasar’s Ghost”, only in this case it’s not an example of assonance, it’s the initials – J.C.
Carlo Collodi didn’t name his Cricket in his book “Pinocchio” – it’s just “Cricket”. But Disney and many of his animators were good ol’ Midwestern boys, and were probably very familiar with the euphemistic “Jiminy Cricket” (They even put the phrase in the mouth of Michael in Peter Pan. He was a London boy, who probably wouldn’t be familiar with the phrase. But it recalled the earlier Disney film, so I’;ll bet they found its use irresistable.), so they decided to name the Cricket Jiminy. If they knew or thought about it, Pinocchio having a conscience with the initials “J.C.” would’ve seemed appropriate.
The bottom line is – if the Houston controllers were pronouncing “Gemini” as “Jiminy”, it’s not altogether inappropriate. There’s a connection there.
*The actual oaths were “Ecastor” (“Ex Caster” = “From Castor”) and “Edepol” (“Ex Pollux”). Castor and Pollux were the Roman names for the Gemini, Kastor and Polydeukos in the original Greek. You can find references to this in a lot of books about Roman culture. And Colleen McCullough used them in the books of her “Masters of Rome” series.