You can borrow from future vacation. And that is what the default FMLA pay status is (VLB). You have to ask for it to be changed to unpaid(FMER). Your CPO can do it or there is a Help Hub function. If you elect your leave to be unpaid then yes, the NJFLI starts right away. If you take FMLA intermittently the state will pay you for every seven day block you were unpaid at work. So you could pick up a trip on your off days - you can not on FMLA days - and just shift the leave benefit.

My wife had surgery this summer. I took intermittent FMLA to care for her during her recovery. I still bid a line every month. I used some borrowed VAC, some scheduled VAC, called off and used sick time (for my own illness), and picked up a couple premium trips on my off days when her mom could help out, and basically brought home right around guarantee when everything was said and done. Because of the seven day block of unpaid time requirement for NJFLI and the way my schedule ended up I was eligible for just 4 weeks of insurance out of the 3 months I was out taking care of her.