That episode of the JHH was called "Secrets of the Muppets" and I have/had it on tape somewhere!
I would have figured for a sentimental end of TMS a good idea could have been to have everyone leaving out the backstage door into the alley, Kermit saying good-bye to everyone as they leave, "See you tomorrow, Beau. Later, Fozzie."
Then, Miss Piggy comes up, "Kermie, dear. Let's not be late for our dinner date!"
"Oh, Piggy! It's only supper!"
"Whatever, dear; let's go! I'm hungry!!"
She leaves out the door and Kermit turns, looks around the backstage, sighs, looks over and flips the switch and the lights go off.
His silhouette is against the light in the alley as he exits and the door shuts. Black screen.
*****
Or to keep it light:
After black screen, we hear little feet on the floor and the light comes on, there's several rats around.
"Are they gone?"
"Yes."
"Well, when the cat's away...!"
Confetti flies around and music begins and they begin partying and laughing.
Fade.