How can I tell which system user Extensions (custom plugins) run under?

A custom plugin is throwing an error indicating 'Shelby - Update user roles' plugin - RemoveUserFromRole (UserId=36961, RoleId=233) - Error - You do not have the 'manage membership' permission that is required to complete this action. 

I thought I knew which user is utilized (based on input from developers), but they all show Administrators role which has suitable privileges (the one in question is marked).

So, where would this be defined?  In the custom plugin, or some other environment variable.