Can you go up there after closing? Like is there a lock or gate that prevents you from going up after it is closed? Or security?

But just outside the gate in the next curve you have almost the same view of the Hollywood sign - 24 hours...

Yes the gate closes and they do have security or police patrolling.

When we were there I saw 2 police officers in the parking lot and 2 park rangers outside the gate. It did look like the gate closes and that they were there to control entrance.

No, the overlook is closed from sunset to sunrise. The gate is locked nightly, thank you for respecting the closure times.

Yes