Renewing a 6 month job hunt ARC

Hi everyone
Was wondering if anyone could give me some info on extending the 6 month job hunt ARC ?
So I have a lot of options a lot of schools want me as I have ten years experience and licensed teacher . I’m pretty sure to apply the work permit they don’t need the health certificate, after the contract is signed and cv and degree and schools info they should then apply the work permit . Then need the health check and country police clearance and some other documents to apply the one year ARC . But this school is telling me I need the health check first to apply the work permit . Please any help would be greatly appreciated!

Is it a regular (public/private) school? If so, you can contact some of contacts in this list.

School Teacher(From 2018 February 8, Work permit application for school teacher shall be submitted to and issued by Ministry of Education.)
https://ezworktaiwan.wda.gov.tw/ezworken/home.jsp?pageno=201802080001

If cram school the school needs your health certificate to apply for your work permit.

Full-time Foreign Teacher in Cram School
https://ezworktaiwan.wda.gov.tw/ezworken/home.jsp?pageno=201508100023&point=tab3

is the 6 month ARC extendable? Me think, its not.

Ok great thanks for the info and yeah it is a cram school . The police clearance can I get it done here in Taiwan or need one from my country . Cause one is already back on its way from my country .