It is normal, or it certainly used to be, to give the vehicle coming up the hill priority, but such niceties are not often displayed these days. On a bike if you were forced to a stop on some of the Hardknott hairpins the ground could be a LONG way beneath your foot and result in a nasty tumble. It is essential to time your run so you don't have to stop if possible and definitely not on a hairpin. I wouldn't ride it in the height of summer.
I've driven hardknott only once and there is one memorable (as in I still wake up in a cold sweat) steep hairpin where all I could see was the bonnet of my car and I had to pretty much guess where the road went. I'm so glad there was nothing coming the other way.