Identification and tracking become important but surprisingly difficult.
First, tag the accounts in the directory so you can identify them as non-user IDs.
Each non-user account needs to be associated with an account owner, someone responsible for securing the system it accesses. Store the owner's identity in the non-user ID's directory entry, so if you go hunting these down later, you know who should be contacted. Remember that owners come and go with employee promotions, turnover, etc., so you might need a department or other organizational tag to go with the employee ID. Group membership can help here. Also, as employees leave, their directory accounts may be deleted, rendering an unknown ID useless - a name is at least someone other people can help you track down.
It may also be helpful to know what machine the accounts are associated with. Keep that information in your directory, too.
If you have a formal request system, where people enter their requirements for requesting the account, the machine, etc., I'd store the request number in the directory entry. But keep in mind that request tracking systems can be changed, and that information associated with tracking numbers issued 5 years ago may no longer be available. I recommend you still keep the owner and machine info on the record, too.
If you don't already have a formal review process for your accounts, consider that when you do implement one, you'll have a big pile of non-user accounts in your directory. This data will help you identify the reviewers (the system owners should review these for appropriateness on a periodic basis.) Consider keeping the review data with the record; you may even want to keep 'last reviewed on/by' information in the directory to provide to auditors.
The main reason to keep this information is in case of a compromise. During the response phase, you need to be able to rapidly identify the people associated with the account so you can change the passwords, scan the systems, and track them down quickly, with a minimum of effort. Keep in mind that you may need to do this activity without alerting the system owners, at least while the investigation is active. You may also need to provide review information to investigators. It's a sad reality that the compromise may originate from an internal source.