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Thank you for the information and your question. Members of the military who are on TDRL are still subject to the UCMJ in the sense that they can technically be recalled to active-duty and court-martialed for misconduct, just as fully retired military members can. However, that virtually never happens and it never happens for something like a DUI. Any cases that have occurred have involved either pre-retirement misconduct or National Security sort of issues. So, you would not have to be concerned with your DUI directly effecting your status.
Please feel free to ask for clarification.