Eclipse IDE SOE Export wizard generates the Dojo widget for custom property page for Manager incorrectly. It misses a pair of double quotes in the Config.js file. Upon SOE deployment, this causes the Map Service Capabilities page in Manager to not render at all.
After the SOE with custom property page for Manager is created in Eclipse, edit the Config.js file in the Resources/<fully qualified SOE name folder>/Config.js file (in the Eclipse project) and surround the value of typeName property with double quotes. SOE exported after this modification will contain correct property page for Manager.