Of course some of the serials had buffoon characters (they were intended for kids, afterall) but I'm talking about COMEDY during EXCITING ACTION and,
specifically, in 'cliffhanger serials' as Cole wrote. John Ford movies are irrelevant to my point. Any sprinklings of humourous moments were filler material before/after the thrills.
Re: Cheeta in Tarzan serials: Perhaps you're thinking of the movies? Even though the number of Tarzan serials is small, the majority didn't have cute, chimpanzee bits because there were no chimp sidekicks! The couple that did have a chimp (not named Cheeta) restricted the comedic moments to their own setpieces - not during the action. (Unless you count shots of a chimpanzee jumping up and down watching Tarzan in peril.
)
Does that look like an action scene to you?
(Not sure if you know but that clip is from the opening of "Tarzan the Fearless" with Buster Crabbe, one of the only Tarzan serials with a chimp sidekick.)
The most one could probably find within an adventure serial would be reaction shots of animals (like the prairie dogs watching the rocket sled in "Skull") or something similar. For anything more than that, we're talking Keystone Cops, etc. territory. There's no character-based wit or slap-stick antics during a fight/chase/trap and dialogue is almost nil.
Indeed, the brilliant "Gunga Din" was ahead of it's time in that regard but again, it is not a serial. Even if you could find an example of humour within action in a 'cliffhanger', it wouldn't have been the norm. Claiming (or defending) the notion that Indy's action-humour was inspired from 'cliffhangers' is an odd thing to champion.