Interesting discussion!
Well, the controller is not the one looking at the TLPD, rather the supervisor to allocate staffing appropriately.
Where I work, that "gadget" is used to schedule the split/bandboxing of sectors, allocation of breaks, rostering of sectors when controllers are valid on more than one group of sectors, and when sectors will be able to be bandboxed for the rest of the day.
That's not to say that we don't have unexpected events, that's the nature of ATC, and that's why controllers go on their breaks with phones so that they can be reached if the need arises
