After being disconnected, the constant running is the pump attempting to top off the two reservoirs in the system. There's one for vacuum reserve (in a sedan, it's inside the right-front fender area just in front of the front door). The other is a pressure tank for the lumbar supports (again in a sedan, it's in the trunk atop the right rear wheel well). Since you have orthopedic backrests, that's a huge demand for air pressure. Over time (especially when sitting for days like you describe), the tanks leak down (or fill up for the vacuum side), and the pump has a full job of topping them off when you restart the car.

The constant switching between pressure and vacuum is the pump's attempt to "top-off" these reservoirs. The programming for the system states that those circuits are low priority, that's why locking/unlocking and putting the car in reverse interrupts the cycling.

I'd cap off the clear line at the pump that runs forward - that's the line for the manifold vacuum assist. See if the pump quits the constant vacuum-cycle. There's a manifold under the passenger carpet, behind a cover plate at the base of the firewall where it meets the floor board. Over time, these manifolds can leak and cause a huge demand on the pump. The part is relatively cheap (under $100) and cured my system of constant cycling on the vacuum side. I also had ruptured lumbar bladders, but I could stop the constant pressure cycling by turning the dials on the seats to 0.

The codes you pulled are there because the pump has (as you say) gone TU. It's taking too long to reach designed pressure/vacuum levels on each of the systems. It also sounds like you've got a blown diaphragm in the door lock actuator for the driver's door.

The circuits in the PSE system fall into 3 categories -
vacuum only (Manifold Vacuum Assist, Rear Headrest release, headlamp level on euro models)
pressure only (lumbar / orthopedic backrest)
vacuum/pressure (locks, backup assist, trunk handle)

I'm pretty sure the design of the system involves pressure/vacuum thresholds which must be attained in a specified time period to prevent codes from being thrown. When you unlock the doors, the system sends air pressure through the lock lines to actuate the (in your case) 2 doors, the trunk lock and the fuel door. As each of the actuators move from locked to unlocked and reach full travel, the pressure builds in the system. If it reaches the programmed cutoff point, the pump cuts off and all is well. If it doesn't reach the programmed cutoff point within a specific timeframe, then a code is thrown and the pump cuts off.

Any of the systems that has a leak will place a huge load on the pump and will cause premature failure of that pricey gadget. I'd check all your circuits for leaks and repair what's required in addition to getting a new or rebuilt (if available) PSE unit.

Circuits that are vacuum/pressure are more likely to leak on the pressure side than the vacuum. On my car, the door locks held vacuum just fine, but when I applied pressure, they leaked.

NOTE that I've constructed a special regulated air supply to test the pressure sides of the system - using your home air compressor risks popping all of those tiny little actuators like balloons. The device allows me to inject air at very low pressures (1-6psi). The system consists of a low-pressure regulator, a gauge, a valve and another gauge. I set the inlet pressure down to about 2psi, attach the device to be tested and open the valve (it's electrical, so I just press a button). If the system has a bad enough leak, you'll hear the hiss. If the leak is slow, when I release the switch, the valve closes and the 2nd gauge allows me to see how the circuit is holding the pressure. Cost about $100 to build, but has saved me many times that in shop fees alone.

The testing spec for the lock system is as follows:
System leakage allowance - at 600mbar pressure or 300mbar vacuum - no more than 30mbar/minute.
Lines and actuators - at 600mbar pressure or 300mbar vacuum - no more than 25mbar/minute.
1 bar is approx 14.5psi, so 600mbar = 8.7psi. For vacuum, 14.24mbar = 1" mercury, so 300mbar vacuum is 21.06 in mercury.

Hope this long post helps