Regarding NJ Family Leave Insurance benefits, if someone has a job as an employee and also runs a business, are they eligible if they take off from the employee job but continue running their business?

Are you full time at the job as a W2 employee?

Yes

So I'm not sure if NJ has something specific, but based on everything I know about these laws, the fact you happen to own a business shouldn't be at all relevant here.

Thank you. I did find this online: https://nj.gov/labor/myleavebenefits/labor/myleavebenefits/assets/pdfs/TDI%20FLI%20Employer%20HR%20Presentation.pdf

"In this case, your answer is correct because it's family leave. It would be the same if he took family leave from full time job but continued part-time job. As a business owner, he doesn't contribute to family leave ins, only employees do. He need not mention is part time work on his own business for purposes of applying for family leave ins because that will be based only on his full time job. Unemployment would be different because even he lost his full time job, they might deny him benefits because he owns a business. For family leave ins, he's fine. You are correct."