This is an interesting question. I can see how Bombadil and even Gollum have some characteristics that fit this archetype. But my gut feeling is that
Davem has put his fingers on the problem we face:
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I suppose Tolkien was walking a fine line in his own mind between recreating what had been lost, & producing what to him would have seemed something dangerously atavistic. The Archetypes had to be presented in a 'civilised' form, they had to be 'dealable' with for a modern audience, & principally they had to conform to his Christian worldview. The Trickster has no place in orthodox Christianity.....
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I agree Tolkien was very aware of such archetypes but was leery of using them in their full blown form. When I first read
Littlemanpoet's question, I was reminded of several things Tolkien wrote about Celtic myth and the Arthurian legends from Letter 131. Here Tolkien talks about his desire to reconstruct a myth that would be dedicated to England:
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It should possess the tone and quality that I desired, somewhat cool and clear, be redolent of our 'air' (the clime and soil of then Northwest; meaning Britain and the hither parts of Europe; not Italy or the Aegean, still less the East), and while possessing (if I could achieve it) the fair elusive beauty that some call Celtic (though it is rarely found in genuine ancient Celtic things), it should be 'high', purged of the gross, and fit for the more adult mind of a land long now steeped in poetry.
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The italics are mine. I think this is where Tolkien signals his intention to part from some traditional archetypes like the Trickster that do have a big role to play in something like Celtic myth. (Or at least I think they do.

I am no expert here at all.) He was aware of these archetypes, and they will influence his characters, but he softens them considerably in an effort to get away from the "gross". I think
Davem is right in suggesting that Tolkien looks at archetype and even faerie through the mindset of his Christian beliefs.
In reference to the Arthurian legends, Tolkien also complained it was too "fantastical, incoherent, and repetitive". Maybe, this too suggests that he was determined to "tame" his archetypes to produce the pure, elusive beauty he wanted rather than having them appear in pure form. Certainly, the "trickster" in its original conception can rightly be labelled "fantastical".
Kuruharan -
I had to smile at your picture of Bombadil going on a rampage! The only way I could imagine him doing this is if he drank too much. Kind of like a northern Dionysius!