Yes, if you have 1099-NEC income from working an outside job then that is self-employment income for you. All expenses that are necessary to earn that income are deductible on your tax return from the 1099-NEC income. So reimbursing the department for use of their car on side jobs definitely counts. Don't enter the amount as a mileage deduction, though. Because you paid it out of pocket to the department I would enter it as car rental costs and just enter the total amount that you paid the department.
@KP63
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