What is the meaning of the highlighted lyrics?
Pick guitar, fill fruit jar, and be gay-o!
Is this a reference to moonshine? Or something else that goes on in the bayou? :dubious: 
I always assumed they are referring to canning preserves. Peel & slice the fruit and add to jar. Add sugar and water. Etc. The exact method is easily found.
My family made a fun time out of it. Lots of hands makes the work go by quickly. Music was played, good conversation while we peeled and sliced.
We did the same thing shelling beans. Get several people together, turn on the radio and get to work. We had a lot of pleasant evenings sitting on the front porch.
You’re close. It refers to moonshine or homemade wine served in a fruit (or Mason) jar.
I’m certain it’s moonshine. They’re talking about having a party, and, well, drinking is more common than making fruit preserves at any party I’ve ever been to.
(Remember to not drink the dregs.)
Different strokes for different folks 
There was no drinking or dancing in my strict Baptist family. Iced tea was the drink of choice. 
Yeah, real close! 
As I earlier stated, it could also refer to wine. The song is about a party in Cajun country and Cajuns, being of French origin, were more likely to make and serve wine than whiskey.
I thought it was “tip fruit jar”. I.e., they’re drinking the moonshine, not making it.
It was a party. People wouldn’t “dress in style” to can, or pickle, food stuff. Fruit jars were strong, plentiful, and would be used for drinking beverages, as well as for storing food.
Thibodaux Fontaineaux the place is buzzin’
Kinfolk come to see Yvonne by the dozen
Dress in style and go hog wild, me oh my oh
Son of a gun, we’ll have big fun on the bayou
They are drinking it, after filling their jars with it.
People (including the Thibodaux and Fontaineaux families) are coming over dressed up, eating good food (like jambalaya and crawfish pie), playing music, acting wild, and drinking out of Mason jars. As mentioned above it’s a party. No one is doing work like canning food or making whiskey.
Thanks for the answers. It is as I suspected.
Back home, I have a shopping bag full of empty Mason jars that I drink out of too. I find it easier to repurpose them than to replace cheap glasses that keep getting broken. 
Perhaps, but it is not intuitively obvious.
Given Williams’ alcoholism and substance abuse, I never assumed there was anything but booze in the fruit jar.
From Wikipedia:
Sucks the magic right out of it.
They could have been sipping a fine Bordeaux or perhaps a Rhone. But somehow I doubt it. Also, does “moonshine” have to be whiskey, especially in that neck of les bois.
That was mainly to confirm that explanation vs some of the others that have been offered.
I have never heard “moonshine” to refer to anything but distilled spirits, usually made from corn mash. The legal definition is “clear, unaged whiskey.” It would never be applied to wine.
Other people might occasionally drink homemade wine from fruit jars, but it’s certain that Hank’s would have been filled with white lightning. Repeatedly.
Technically-speaking, moonshine is raw alcohol that measures around 180 proof (90% alcohol). Whiskey is moonshine that has been tamed. Aged in blackened (burnt) oak barrels for years, and cut with distilled, filtered water. The charcoaled oak allows the whiskey to breath, and removes impurities from the raw alcohol. Old whiskey barrels are sometimes used to make scotch.
What a coincidence, the first thing I saw this morning on my FB page was a clip from 1965 ‘Shindig’ with Leon Russell and Glen Campbell singing ‘Jambalaya’! Black and white and poor resolution, but they looked darn cute, about 20 years old!
I heard the song on the radio just a couple of days ago, and I thought about how clever and fun the lyrics are.
Son of a gun, gonna have big fun on the bayou.