Green’s Dictionary of Slang

1. to fondle or indulge to excess, to tend carefully, to cherish.

1560		Nice Wanton Ci: Ye winked at their faultes, and tidled them alway.
1748		Richardson Clarissa I 291: To leave the family-pictures from his sons to you, because you could tiddle about them, and tho’ you now neglect their examples, could wipe and clean them with your dainty hands!

2. (also tiddly) to fidget, to ‘mess around’, to play with trifles.

1929		J.B. Priestley Good Companions 539: Here, this looks a good number. Just tiddle it quietly, will you, old boy?
1945		D. Bolster Roll On My Twelve 56: I see: you wanted to tiddly it up a bit before I saw it.