Green’s Dictionary of Slang

1. to shake about, to tumble.

1709		Cibber Rival Fools III i: I’gad I’ll fetch one then, shall jerrymumble you.
1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue.
1811		Lex. Balatronicum.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.
1834		‘Jack Downing’ Andrew Jackson 43: In this skrimmage there warn’t any child’s play I tell ye [...] they was all jerrycummumble in a heap.
1890–1904		Farmer & Henley Sl. and Its Analogues.

2. as jerry-cum-fumble ext. of sense 1, and quasi-rhy. sl. play on tumble v.¹ (1) and, since speaker is an older man, fumble v. (1)

c.1850

Peeping Tom (London) 14 54/1: ‘I should dearly like to jerry-cum-fumble you.’ ‘ [...] ‘Good gracious what is that?’ ‘Oh! a most delightful exercise [...] jerry-cum-fumbling puts new life into us’.

3. to understand, to work out [tumble v.² /rumble v.² (1)].

1989

J. Morton Lowspeak 80: Jerry – wideawake or shrewd. [...] Jerry-cum-mumble = tumble = understand. Probably obsolete since the Second World War.