Except for fact that if you shoot one you'll virtually alway get its mate because they don't bugger off, I haven't seem hairs do what the OP'S describe.
Plenty of rabbits running towards the spotlight and disappearing underneath the ute.
Sadist thing (depending upon your point of view of course) was in Oz. Our family was sitting on a raised brick terrace out front in the middle of the day when a rabbit came thru our front gate and continued in a straight line towards us until, thud, it hit the terrace. It's eyes were completely closed and matted with myxo puss. I had the honour of disposing it. No one else wanted to touch it.
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