What should be the normal behavior of the pump?
Standard behaviour of the pump is to run for at least seven seconds when the driver's door is first opened. If the door is reopened a few minutes later, the pump may run again for a shorter time (since the system is already close to the correct pressure).
With the engine running and the car driving, it's normal for the pump to run every three or four gearchanges. Again, the pump should run for about five seconds at a time. Then it should be silent for some time while gearchanges are not being made. I would expect it to run maybe once every 10 minutes?
I'm not sure on all these times exactly, but it should give you some idea.
Watching your video - that sounds completely wrong, sorry
I think it needs to be hooked up to Alfadiag or FIAT Examiner to see what is happening with the pressure. I reckon if the pressure is spiking, perhaps it is the accumulator faulty rather than the pump. The accumulator is a gas-filled black canister (mounted on the actuator but replaceable separately). When the pump runs, it pressurises the fluid against the accumulator. If the accumulator is 'dead' (has no pressure), the fluid pressure would go very high (fluid can't be compressed), so the pump would run only briefly.
I don't want to disagree with David C, it could be the pump at fault, but I'm just trying to give you food for thought.