It's the right place

Whether they fire you is dependent on the rules and the laws in your state. A lot of states have "at will" which means employees have very little rights. If they don't want employees there at 3am they should probably use badges. Why would they know it was due to a mental illness? You only need to tell them you needed to get your wallet. If you have said anything about illness I don't think I would. If they think you're drunk and are concerned they can give you a drug test (which does not mean you disclose any meds).

Reason would say if you have never given them reason to doubt you they will just forgive the incident. You can laugh off the 3am part with being quirky or something. Einstein was up at 3am all the time. Tell them you're related.

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