In Season 3, episode 2 of the sitcom Modern Family, Phil uses the expression "Good governor" to express his incredulity when he realizes that his wife has an obsession about proving she is always right. I presume this is a variation on "good grief" and similar exclamations but wonder if anyone is aware of the origin of the use of the word "governor." Is it a Britishism that has entered US English, from the informal use of "governor" ("guv'nor) to talk about a person in a position of authority?
The template for "good grief" and similar is "good Lord!", "good God!", and similar apostrophes addressing religious figures, whether believed in or not, as exclamations. Some have been contracted such as bloody from "by Our Lady" and the now obsolete zounds from "God's wounds".
The origin of these in turn is from making oaths and vows over trivial matters, "By the good Lord, I swear I've never seen such a thing!"
Such references to religious figures is considered a breach of the Third Commandment, "Thou shalt not take the name of the Lord thy God in vain; for the Lord will not hold him guiltless that taketh his name in vain." (Exodus 20:7).* And hence a sin, and certainly not polite language. It is from this that we get swear used of all offensive language, including sexual swearwords like fuck, and lavatorial swearwords like shit that have no religious connection.
Such use has been with us for a long time; Chaucer's characters can't go more than ten minutes without making a very extravagant oath showing remarkable knowledge of hagiography, and all European languages seem to have their equivalents (Mon Dieu! [French], Gott im Himmel! [German] and so on).
They are though the sort of expressions that will get children punished by their parents. They're generally considered mildly offensive, less so than sexual and lavatorial swearwords, but still offensive. Some religious people might consider them more offensive than other swearwords, because of the Third Commandment mentioned above.
For this reason, it's to be avoided in at least some circumstances, so we have inoffensive alternatives, one catches oneself about to say "Shit!" and instead says "Sugar!", or one catches oneself about to say "Good God!" and instead says "Good Grief!". Eventually, these have become exclamations with their own currency.
So, either the character is one who would want to avoid a more offensive term, or the writers substitute in a milder term so as not to upset viewers, or both. (I don't know the show, so don't know if it's one where other characters would use stronger language).
Now, guv'nor as you say, is indeed a Britishism, particularly in South England. It's much less common than it once was, which is one reason to suspect it's not the source. Another reason is that while guv'nor places the addressee in a higher position than the speaker, they don't place them so high as to be sworn by. (Sworn at is a different possibility). There's no such British use of guv'nor in exclamations.
Another thing to consider, is that in the current age, governor has very little use in formal British English, but much more in American English, where governor is the highest office in each state, and many with high Federal office, including presidents, have been governors in the past.
A final thing to consider, is that while there are some common mild non-swears of the "Sugar!" and "Good grief!" variety, there is great variety of them, and an even greater variety in fiction, where writers have fun (and amuse their audiences) with thinking up new examples.
In all, not a Britishism, not common anywhere, quite possibly a one-off invention of the show you are talking about, but following a very common pattern.
*Some, like the Quakers, would take any oath for any non-religious reason to be a breach.