Yep! The damper motor is the culprit! 5 years ago when I bought my Trek with the same microwave mentioned here, it stopped at the 59 second mark every time. I replaced both the microswitch and the damper motor and haven't had a issue with it since. Send me you email in a PM and I'll send you the document (with pictures)another RVer shared with me after fixing his.
Don Ford
2004 Safari Trek 31SBD (F53/V10 20,500GVW)
'09 HHR 2LT or '97 Aerostar MiniVan (Remco driveshaft disconnect) for Towed vehicles
BlueOx Aventa II Towbar - ReadyBrake Inertia Brake System