NY and NJ do not have tax reciprocity. NJ has reciprocity only with the state of PA.
If you are a resident of NJ, all your income is taxable by NJ, regardless of its source. A resident of NJ (or FL), is taxed by NY only NY-source income. See this reference for details:
https://www.tax.ny.gov/pubs_and_bulls/tg_bulletins/pit/ny_source_income_nonresident.htm
You can't just choose to be a resident of one state or another. State's have rules regarding residency. You can read NJ's detailed rules on determining residency here:
https://www.state.nj.us/treasury/taxation/pdf/pubs/tgi-ee/git6.pdf
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
