'Time-to-empty signal' is a buzzer that goes off (an alarm sound) , or a light that flashes, to tell you that the vacuum cleaner is full of dust and it's time to empty it.
Here's a text explaining 'positive agitation':
https://vdta.com/Magazines/SEP10/fc-GaskoSep10.html.
It appears to be a term specific to vacuum cleaner design.