If any council member or other officer or employee of the city shall, after lawful notice or process, wilfully refuse or fail to appear before any court or judge, any legislative committee, or any officer, board or body authorized to conduct any hearing or inquiry, or having appeared shall refuse to testify or to answer any question regarding the property, government or affairs of the city or of any county included within its territorial limits, or regarding the nomination, election, appointment or official conduct of any officer or employee of the city or of any such county, on the ground that the answer of such council member, officer or employee would tend to incriminate him or her, or shall refuse to waive immunity from prosecution on account of any such matter in relation to which he or she may be asked to testify upon any such hearing or inquiry, the term or tenure of office or employment of such council member, officer or employee shall terminate and such office or employment shall be vacant, and he or she shall not be eligible to election or appointment to any office or employment under the city or any agency.