Just to drive the point home: Language is fluid, English has no organisation setting any rules and we the people get to decide how we pronounce things. And we've pretty clearly decided on what way we want to pronounce gif.
the "correct" pronunciation is whatever the community decides, despite what we may individually think of it.
As such "jif" is decidedly _not_ the "correct" pronunciation because essentially the entire community says "gif"
"jif" would be the "archaic" pronunciation. Technically valid, but not used by anyone except for hold-outs and people who refuse to accept modern pronunciation standards.
But, everyone pronounced it with a short 'i' and now they've adopted that in adverts - 'Every little [lidl] helps' - doesn't work if you pronounce it Lie-del!
If they wanted it pronounced Lie-del - they should have spelt it like that - Lidle!