Here is where I store my Handy Man (Hi lift) jack on my 1966 CJ5.
It has rested here for many years with no problems. It stays relatively
clean and fairly accessible. The shovel just in front of the radiator doubles
as the jack handle. The climbing pin mechanism is in a bag in the tool
box under the passenger seat.

The only problem I ever had was when I left the climbing pin mechanism on
the jack. It once got tangled up with the throttle linkage.