It was generally called cadence back in the sixties also. Jody was a catch-all name for the guys back on the block who was dating your girl, working at your job, and/or generally living the life from which you had been so rudely removed.

However, much of the cadence of my era (and, I assume, others as well) was pulled from the popular music of the time. For example, a Vietnam cadence was done to the tune of "Poison Ivy"

They say there is a pla-ace
A-Way across the sea
That's where they wanna bury me-ee-ee-ee-ee.
In Vietna-ah-ah-ah-ah-ahm
Vietna-ah-ah-ah-ah-ahm
Late at night when your sleepin'
Charlie Kong comes a creepin'
All arou-ou-ou-ou-ound, Vietnam.

Also there was that Airborn ditty done to Bo Diddly's Bo Diddly

Bo Diddly, Bo Diddly, Have you heard?
I'm gonna jump from a big iron bird.
Stand up, hook up, shuffle to the door,
Jump right out and count to four.
If that chute don't open wide,
I got another one by my side.
And if that spare don't open wide,
Guess I'm in for a hell of a ride.
Lay my arms across my chest,
Tell the girls I did my best.

There were probably others.