Am I understanding this correctly?
You log in as the administrator and schedule a job. You then log out and log in as another user to lock the administrator. The job runs after the admin ID is locked but your trace log doesn't show it? Did you start the trace after you logged off of the administrator ID? Isn't the trace log created when a user logs in. If the ID is locked and it's only a job running, I wouldn't think it would log anything.
Try setting your trace to 10 instead of 2. My question would be, how is the job running on an ID that is locked? Makes me wonder if the job is running under another ID, hence no log file for on the job under the administrator.