Work permit for LTVP holders

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Hi,

I am LTVP holder, which is granted for mothers whose child is studying in Singapore on a student’s pass.
I'm looking for a part-time job, but it is difficult due to my rare visa status.

According to MOM, my employer can apply for a Work Permit for me, under which I can work in any sector. So, I approached a recruiting agent for part-time accountant jobs. But he told me he has never seen such work permit, and mothers like me usually apply for EP or S pass.

I need a part-time job as I am not yet prepared for full time work.
Does anybody know anyone of the same situation and succefully got a part-time job?
What kind of jobs are these?, and where did they find the jobs?

Please help,