hi. i had this same problem. i wanted to fix an ipad mini 3, (careless of touch id working) the home button flex was ripped apart and had no connector end any more. just the original home button end (included button itself).
using a mutimeter located the two pins that activate the button on the flex. ( second and third on the side nearer to the home button)
once i had those i was able to solder thin wires .
what i thought was the hardest part, it became the easiest (the motherboard side) i remember, on ipad and ipad 2 and ipad mini. home button sense is just GROUND !!! so i grounded the first pin from the home button connector on the motherboard and it worked!!! this is the first pin closer to the battery connector.
which it means you just need to run a wire from there to home button and the other pin from home button to GROUND :) so when you push the home button just GROUNDS that pin.
i have pics that i cant paste here. but please emailme to: email@example.com
be glad to help