How to start 1099-NEC for spouse and separate for myself. This is not my business. It is owned/operated by non-profit organization

You are going to enter this as self-employment income.  I know, you don't have a business.  But the non-profit is paying both you and your wife as contractors.  That's why they're using 1099-NEC forms.  And contractors are always self-employed.  

So you will scroll down in the wages and income section of your federal return until you reach 'Business Items'.  Click start next to 'Business Income and Expenses' and then the system will ask you if you had income from a 1099-NEC.  You'll say yes.  

The system will walk you through all of the necessary steps to file the return as a self-employed contractor.  One of the benefits is that you can deduct expenses for anything that you had to buy in order to do the job for the non-profit.  

@kthomp5