I've lived in Texas for most of my life and never heard an outhouse called a thunderbox.
Sound like something made up by a bad Hollywood screenwriter working on his first western--"I don't need to go heeled to get the bulge on a tub like you. Skin that smoke wagon and they'll bury you behind a thunderbox!"
(For the record, I like Tombstone and watch it at least once a year but awkward euphemisms are a distraction. Watch carefully for when Val Kilmer stabs Frank Stallone in the arm. And what's up with the fat Billy Bob Thornton?)
I saw these arty crappers at the rodeo, and thought they were cool.
If you really want to impress me, add a working sink and one of those compact DVD players.
And an air conditioner.
And a lock on the door.