Precisely, a foreign spouse needs to have been granted residence (且獲准居留者) to have working rights by virtue of being married to a ROC national with household registration in the Taiwan Area. Under the Immigration Act, residence for foreigners refers to being granted an ARC. It is even a contentious issue whether APRC holders married to ROC nationals need a work permit.
In fact, a resident visa (or any sort of visa) will be entirely irrelevant from the moment the foreign spouse has been granted an ARC.
就業服務法第48條第2款：雇主聘僱外國人工作，應檢具有關文件，向中央主管機關申請許可。但有下列情形之一，不須申請許可：外國人與在中華民國境內設有戶籍之國民結婚，且獲准居留者。[1]
Yeah, don’t even get me started on that one.