I have an outdoor light controlled by a pair of 3-way switches, A and B. The switch B is much closer to the light.

Here are the behaviors I observe.
    
    During the day:
    A: Up     B: Up or Down    Light:ON
    A: Down   B: Up            Light:ON
    A: Down   B: Down          Light:OFF

    During the night:          Light:ON (regardless)

Also, believe that the light comes on at a certain hour. So it must be on a timer and not on a light sensor. However, I cannot locate the timer.

The wiring on switch B is attached.

I'm assuming I'm correct that the timer is involved. However, I still cannot make sense of the wiring and so I cannot figure out how to change it to make the three-way switches act normally during the day.

[![enter image description here][1]][1]


UPDATE: I've disconnected the wires and here's what discovered. The power comes via one of the 14/3 wires. The black is always hot. The red is hot during a few hours of the night (but not dusk to dawn. More like 1am-4am). Does this confirm that there's a timer somewhere along the way? What could it possibly look like?

UPDATE: Mystery solved:
[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/HywwM.jpg
  [2]: https://i.sstatic.net/S3pa1.jpg