Oh, the things one can find on YouTube...
You may have noticed a little item in Jack Kelly's filmography called What About Linda? This was an hour-long syndicated TV appeal for the 1961 March of Dimes campaign. It starred an adorable tyke named Linda Breese of Columbus, Ohio.
Its TV Guide listing says: "The March of Dimes sponsors this filmed show which features its 1961 poster child, Linda Breese. Linda gets lost on a Hollywood television set, and we see many stars, including Louis Armstrong, the Kingston Trio, John Raitt, Debbie Reynolds, the Crosby Brothers and Lee Marvin interrupting their acts to look for the little girl. Robert Cummings is host."
No, I didn't find the whole show, but I found the next best thing: the four-minute preview for the show. JK appears briefly, not as Bart Maverick, and not exactly as himself, either. And, he's a riot!
I hope someday his entire appearance can be found. Anyway, JK shows up at about 1:54. But, I suggest you fight the urge to fast-forward there the first time you watch it and just let the preview unreel from the start, because there are many other familiar faces I'm sure you'll enjoy seeing. :)