This is a specialized tool used to polish watch pivots called a Jacot tool or Jacot lathe. Significant pivot wear and corrosion can greatly impact watch performance. There’s much more to quality vintage watch servicing restoration than cleaning and oiling. Serviced is supposed to mean a complete regimen of full disassembly, inspection, adjustment, repair, optimization, and testing. Many watches need a good deal of work to bring them back to where they belong— strong running and reliable.