You would be correct to file a NM non-resident return. NM taxes non-residents on income derived from employment within NM.
As you have apparently already discovered you would then claim a credit on your WI return for taxes paid to another state.
If you are not already doing so you should have your employer withhold taxes for NM and not WI. That way you will not have a big NM end-of-year tax liability since you would have paid it during the year. If NM is already withholding you might consider increasing that.
Here is the NM reference.
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