So, "jod" is hilarious, but "jift" is disingenuous?
I don't get it, but I guess it's fine.

Also, I was trying to go by the fact that "gift" has the same 2 letters after the 'g' as "gif", which tends to be an often stated thing when people try to make a semblance of logic^[people tend to look at the previous and next letter, and if that one is a consonant, then maybe also the 2nd, previous and next letter.], explaining why something is pronounced the way it is, in English (and then also used in comedies, where all of that logic fails due to exceptions everywhere).

For pronunciation in the English language, I consider that there is often not a logic behind it, but a history. And from that POV, "jif" would be the correct one (∵ the creators). But I still pronounce it "gif", because:

• it's an acronym, so I consider the pronunciation to not be very important and it is better to go with what clicks in my mind faster ^[Not many people go around arguing 'nome vs G-nome, right?]
• I first read .gif in a file name and there was noone to tell me how it was pronounced. I went with G.I.F. until I felt like calling it "gif" with the logic of "gift". Then again, I heard quite a few people call it "gif" and it set in.