(Sunset time - Sunrise time) /2 = Zenith?
(19:47 - 7:07)/2 = 12:40
Is this true for all days?
Your phrase “zenith time” is somewhat misleading, because in most locations on most days the sun never actually reaches the zenith, i.e., the point directly above the observer.
What you mean is “true local noon”, the time at which the sun crosses the observer’s meridian (i.e., the semicircle extending through the zenith and the north and south points of the horizon).
And yes, the time between sunrise or sunset and true local noon is always half of the time between sunrise and sunset for that day. (See a graph of the simultaneous variation in these time intervals here.)
Isn’t the equation (19:47 + 7:07)/2 = 1:27 ?