I am from Florida and do not plan on leaving. However, I have a vacation home in North Carolina. I spend less than 183 days in North Carolina, but spend some time working in my home office for my Florida business in North Carolina. Am I considered a resident or non-resident and which type of state tax return do I need to file?

You are not a full-time resident of North Carolina as per the definitions in the North Carolina administrative code. You are there less than 183 days and domicile from another location. However, if you generate income from North Carolina sources, you would be required to report that income on a non-resident North Carolina tax return. If you do not generate income from North Carolina sources, then that is different, but that doesn't appear to be the case.