When you are interpreting you forget about “time and space”. That is why it would make more sense for the interpreter who has just finished interpreting or is going to interpret next [depending on how many interpreters you have in the booth] to reset the timer.
For example if your colleague has started and you need to interpret next, reset the timer so that the chime 1 minute before the end of the shift will remind your colleague to handover.
agree in advance before the event starts who is going to reset the timer.