A skittish pony is one that is characterised by unpredictable, unstable behaviour, usually because of nervousness. A skittish investor is one that is over-cautious or who quickly pulls out of a trade or deal. Merriam Webster.
The common denominator appears to me to be the unreliable characteristic of man or beast, resulting in unpredictable behaviour.
There is a noun, skite, with an accompanying verb, which the OED lists as part of Scottish and 'Northern' dialect.
'On the skite' is Scottish for being drunk. 'A skite' is a ricochet or a glancing blow.
I wonder if the unreliable nature of an inebriated person or a sideways blow or a glancing ricochet indicates that 'skittish' originates with 'skite'.
The vulgar verb 'skite', to defecate, is very obscure and the Australian/New Zealand meaning of 'skite' - 'boastfulness or conceit' seems to be unrelated, but the Scottish use of 'skite' or 'skyte' as someone who babbles or 'blethers' without logic or consequence may also have a bearing. All from OED
Does 'skittish' derive from 'skite' ?