Does your Jeep have a lift?
You can buy a rebuild kit for that, I bought one on Amazon a few years ago. It's not to bad of a job, but if your Jeep has a lift then you might need a new driveshaft.
Would explane why his brakes still work good, if the brakes didn't or had a hard pedal then he would know the pump wasn't working. When the pump kicks on when first started would be because the vacuum in the booster was to low.
My guess it would either go to the frame or the body.
Where do the 2 cables go to that are where the nut and big washer is to the left of the broken strap?