I am in same position. When I spoke with Social Welfare, the answer was that JSB is for job seekers, not self-employed.
When I said that I was still actively seeking EMPLOYMENT, whilst trying to test market if I could generate business as a self-employed, I got no joy - stock answer - JSB is for those seeking employment.
I suggested that as soon as I received any income from self-employment I would cease claiming JSB, thereby saving state money. I still got no joy.
Probably not what you want to hear.
With regard to question, can you be part time self employed and part time looking for a job, if you get a definitive answer, I'd love to know.