capital gains - state allocation

No.  It appears you meet the definition of non-resident for NJ.  Your domicile is FL and you spend less than 183 in NJ.  Therefore, you should be filing a non-resident return for NJ income earned while physically in NJ.  The other income/gains are allocated to your resident state.  

Here is a list of items of non-resident income subject to NJ tax.

Income of a Nonresident Subject to NJ Tax. Some examples of income taxable to a nonresident include:

1. Wages, salaries, tips, fees, commissions, bonuses and other payments received, whether in cash or in property, for services performed in New Jersey;

2. Profits and other income from a business, trade, profession or partnership conducted in New Jersey;

3. Rents or royalties from real and tangible personal property located in New Jersey or from other business activities in New Jersey;

4. Gains from the sale of your principal residence or other real estate located in New Jersey;

5. Winnings from a casino or racetrack located in New Jersey;

6. Prizes won in a lottery, drawing or other contest in New Jersey (other than the New Jersey Lottery);

7. Income of a New Jersey S corporation allocated to New Jersey.