Argle Bargle in mid-Fargle

Solution 1:

argle-bargle is Scottish slang

verb argle-bargle (third-person singular simple present argle-bargles, present participle argle-bargling, simple past and past participle argle-bargled) (slang) To argue.

1886, Robert Louis Stevenson, “The Captain Knuckles Under”, in Kidnapped, being Memoirs of the Adventures of David Balfour in the Year 1751: […], London; Paris: Cassell & Company, Limited., OCLC 1056292939, page 97: Last night ye haggled and argle-bargled like an apple-wife; and then passed me your word, and gave me your hand to back it; and ye ken very well what was the upshot. Be damned to your word! https://en.wiktionary.org/wiki/argle-bargle

Also see this - https://www.dsl.ac.uk/entry/snd/arglebargle_n_v

I don't know what fargle is. It could be a nonsense word just used for rhyming purposes. Do you have any more of the text?

Solution 2:

The Dictionary of the Scots Language has an entry for Argle-Bargle meaning:

(adv.phr.) In disputatious talk.

• em.Sc. (a) 1931 J. Ressich in Gsw. Herald (8 Aug.): And on they gaed, argle-bargle, an' the crood got bigger an' bigger.

as for fargle, the following site suggest it refers to a game:

fargling is any game which is used to resolve a dispute between two or more people. Now it probably wouldn’t work too well at a UN Security Council meeting but it’s perfect for determining who gets the first turn on the swing.

The classic American fargle is rock-paper-scissors, which is also known as roshambo.

(wordfoolery.wordpress.com)

So, according to context, the whole sentence might refer, for instance, to a dispute over a trivial issue.