It looks like one of those “vague, unsure” ones, it’s perhaps too old a word, and with too many vague, possible sources.

Some bits of dictionaries suggest various etymologies - it likely drifted from words in Gaelic, Scots, Arabic and French, like “jupe”, “jump”, “juppe” “jubbe” and so on, which tended to mean things like “smock”, “jacket” or whatever. It’s been around in English for various clothing types for a few hundred years, and referred specifically to the woollen pullover thing from the picture above for 100-150 years.

It has no relation at all to jump as in “leap”.