I love taking apart these bosch made creations. There's a lot of clever tech inside. The module has a rotary sliding vane pump and a large solenoid valve to control airflow. There's a little heater which is used a reference for airflow in the pump as it cools once heated. My fault was the the resister wafer showed as an open resistance, causing the fault. I disassembled the entire unit, remove the motor pack, don't let it come apart and lose the pieces. Disassemble and I applied some liquid deoxit to the sides and reassembly shows now measured at 45 ohm.
Cleared the fault, no longer back.
Didn't see anyone else online document they took apart and repaired these, so here it is. I see many E53's with faults on this module, some of them are able to be repaired inexpensively without buying a replacement.
see album.
https://photos.app.goo.gl/pumxtiz8W9LPyTbq6