Unless you are down to 10/12 big blinds, then no hand is allin pre flop. Why risk tourney life in what will be essentially a coin flip.
why does your stack need to get to a 10-12 bbs before you get it in preflop to accumulate chips?
not saying you need to get it in 100+ bbs deep with jj, but what about 25-40 bbs? it may not be an open jamming stack sizes, but they're good for re-jams / squeeze jams. you can pick up a ton of dead money and you have good
equity against most call ranges if you go heads-up, especially since you get to see all 5 cards.
also, even if jj's equity is a coinflip when all-in preflop, why do you wait until your stack is low before your willing to take that coinflip. equity is the same, so
odds of you winning / losing are equal, but the difference between losing 10 bbs / winning 20 bbs vs losing 25 bbs / winning 50 bbs is that 50 bbs will get you much deeper in mtts. the risk is still the same, but your overall mtts results will differ as 50 bbs will provide way more options and allow you to 'survive' much longer.
survival in mtts is important, but so is chip accumulation. you can survive a long time in mtts by just folding, but that doesn't really help you. plus, you're not just playing jj, but a range of hands. so, you'll actually be jamming wider with 10-12 bbs. so, you might find yourself jamming a hand with less equity for less chips when you could have gotten it in a hand with more preflop equity for more chips.
anyway, not telling you what to do, just something to think about as you could be severely handicapping your results if you wait until your short stack to play your big hands for max value.