This old man ... what is "knick-knack?"?

My initial guess was that "knack" meant knowledge, wit, or trick, but wiktionary list "knick-knack" as "a small ornament of minor value," which could have meant a small toy or a game.

Let's try parsing the lyrics in lines 4-5.

"He played knick knack on my thumb

with a knick knack paddywack give a dog a bone"

A comparison with the 1870's song Jack Jintle collected by Anne Gilcrest (Anne Gilchrist) shows that "the old man", "paddy whack" (back formation from Paddywack?) and "giving the dog a bone" are not essential features of the song.

"And I can play nick-nack upon my own thumb.

With my nick-nack and pad-lock and sing a fine song"

Hence the sentence in question can be parsed as follows (SVO/M1/M2):

"He played knick knack / on my thumb / with a knick knack paddywack",

and the corresponding verse in Jack Jintle as follows (SVO/M1/M2):

"I can play nick-nack / upon my own thumb / with my nick-nack and pad-lock"

From the comparison, guessing becomes less uncertain: knick-knack (nick-nack) is a small ornamental object that is being played (spun?) on a tiny, difficult surface such as the child's thumb or shoe.

Paddywack need not be the angry Irishman or even a pad-lock but it can be any small object that requires fine motor control for the child performing the song and the game of knick-knack.

We could also imagine that the song was intended to encourage young children to develop their verbal skills and motor skills akin to the kind of skills that are fostered in today's kindergarteners and younger school children.

Knack Definition

knick knacks are two animal bones held between fingers and thumb which when shaken can produce all kinds of tunes after some minimal practise. I played them as a kid. I have also seen them played on stage by professionals. I am 79.

Knick-knack refers to a tiny ornament of little or no value; a trinket.

In this case, 'knick knack patty whack' would mean an unimportant bullying Irishman with little or no value.

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This Old Man Lyrics

i always thought it was a rather crude poem. and my mother confirms it! you can make up your own assumptions however.

some say it is a rhythmic tapping? as he plays it on his thumb/knee etc. however, most say it is just a nonsense rhyme (like most nursery rhymes).

WELL IT IS SMALL WORTHLESS OBJECTS, ESPECIALLY HOUSE

HOLD ORNAMENTS