In the California Digital Newspaper Collection there are numerous mentions of young men sucking their canes.The earliest is in the Sacramento Daily Union of July 29, 1871: In a theatre story, the reporter wrote: ...  If anybody did, perhaps it was Hal Delamayne, who sat on the corner of a table, in front of the footlights, in true stage pose, swinging his foot and sucking the head of his cane, while he stared down the first row of empty chairs in the parquette. Perhaps he was thinking of how bright it had looked last night,....  My personal favorite is in the Humboldt Times of March 13, 1885 (Tom Sawyer was published in 1876), which reads as follows:
 We now know why dudes like to suck their canes so well. The latest style of walking stick is made of Bamboo, porcelain lined and filled with rum When the temperance people see a young man sucking the head of his cane they don't want to laugh at him anymore—they want to nab him.  Another article has a young man sitting in a car sucking the head of his cane while a woman is standing. I didn't read any more of them, but noted the first reference to the question "sucking the head of his cane" was dated
In a message dated 7/15/2023 10:21:47 AM Pacific Standard Time, [log in to unmask] writes: 
https://forum.wordreference.com/threads/sucking-on-their-cane-heads.1475922/

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From: Mark Twain Forum <[log in to unmask]> on behalf of ben <[log in to unmask]>
Sent: Saturday, July 15, 2023 10:02:06 AM
To: [log in to unmask] <[log in to unmask]>
Subject: sucking cne heads

I'm reading The Adventures of Tom Sawyer, in chapter 5 it read "...for they had stood in the vestibule sucking their cane heads, a circling wall of oiled and simpering admirers...", I don't quite understand what the young men are doing, is "sucking their cane heads " a metaphor? Can someone explain it?
Tks