Oh… for crying out loud 
… OK, a bit of a face palm for myself… and big a “why the bleep didn’t you add in this little tidbit at the beginning” for you 
The widget DOES show either - -:- - or 00:00 depending on how you use the reset function…
In my limited defense, I really don’t use the Time Input Widget for my projects… nothing I use requires such specific timing… so while I did poke at the reset for the purposes as I described above, I never actually SAVED the reset settings and thus never noticed what you only just now mentioned.
Therefore… if you actually want to use the reset as a null time for whatever reasons that you still haven’t made clear, then use the Boolean results from these two commands to determine if the Start/Stop time is - -:- - (there is a NULL after all 
just not in the actual time calculations) or 00:00 (midnight).
t.hasStartTime()
t.hasStopTime()
E.G…
BLYNK_WRITE(vPin) { // Time Input widget Scheduler
TimeInputParam t(param);
if (t.hasStartTime() == 0) {
// Start time is NULL
// do NULL stuff
} else {
// Start time is valid number... including 00:00
// do start time stuff
}
}