If Section 1402 applies, you will want to enter as Miscellaneous Income so the Schedule C is not needed/ no social security/Medicare tax.  Instead of entering as a 1099-NEC, Enter under Miscellaneous Income.   (I would use "Section 1402 Village payment" as the description.)

If you want to challenge the classification, see Independent Contractor or Employee?  or contact the Village directly for an explanation.
 

Internal Revenue Code section 3401(c) indicates that an “officer, employee, or elected official” of government is an employee for income tax withholding purposes. However, in some special cases the law or a Section 218 Agreement may specify otherwise.

Regulations for section 1402, addressing the applicability of self-employment tax, indicate that performance of the functions of a public office does not constitute a trade or business. Therefore, holders of “public office” are not subject to self-employment tax.

See Tax Withholding for Government Workers 

As an elected official, I receive a W-2.  It is not my primary position.  I have a home office that is used strictly for that position.  I am also not reimbursed for mileage or use of my vehicle for that position.  Do I use the Form 2106 to receive discounts on my taxes?

Yes.  But gaining deductibility will be at the state level return.  If your state allows miscellaneous itemized deductions, then you would possibly be able to deduct the expenses.  With the changes from the 2018 Tax Cut and Jobs  Act, employee business expenses were eliminated as a deduction on your Federal return.  If you live in Alabama, Arkansas, California, Hawaii, Minnesota, New York, or Pennsylvania, there is a deduction for unreimbursed employee business expenses.  Or, if you live in a state the still allows itemized deductions even if you took the standard deduction on you Federal return.  Click here for more tips on working from home.

The pandemic has affected your taxes in many ways. Including reporting in TurboTax the amount of stimulus money you received. Click Here for more information on how the Pandemic affected your 2020  taxes.