Does your taxpayer work for the corporation, or is only a Director? Director pay isn't the same as being an employee.

1099-Div = not deductible for the C Corp, reportable (like an investment) for the shareholders (you only told us this is an officer)

1099-NEC = when this is a vendor (supplier of goods and/or services) to this C Corp being paid, by running a different company that is a sole proprietorship. Directors (not working for the corporation) also get a fee reported on 1099-NEC.

"who are usually either on payroll"

Yes, that is the requirement for Corporations, they are an employee to their entity.

"or issue a 1099 NEC for themselves (as owners)."

No one is ever issued a 1099-NEC from their own entity, as owner, for the work they did related to that entity. When you see this, it's someone trying to bypass something required or simply doing it wrong.

See the IRS references:

https://www.irs.gov/businesses/small-businesses-self-employed/paying-yourself

There is Sole Prop, not 1099-NEC and no payroll. There are partnerships (Form 1065), no 1099-NEC and no payroll for the partners. There are corporations (or electing to be treated as a corporation) and that = payroll if you are working. Shareholder dividends is it own topic, for C Corp.