conductor's baton
Specifically the baton used by an orchestra conductor. The Japanese term 指揮棒 is a near synonym but タクト is more common in everyday speech.
from German Takt(stock)
See also: 指揮棒
When the conductor brought down the baton, the performance began.
tact system
Borrowed from German Takt(stock), meaning 'baton' (literally 'beat stick').