Pressing door will override timer setting and manually turn switch ON-OFF.
Press door or open timer door, and press any of 4 buttons located in corners.
You know information posted so far:
However, you are moving the small switch from Timer to OFF.
And when switch is OFF, the override does not work because circuit is OFF.
You want a timer that can switch programming OFF, and not switch circuit OFF, so that device toggles between timer and ordinary switch.
Looking at timers on the market today, I cannot think of any in-wall programmable or box timer that does what you want. Each has manual override that reverses timer function, but when you set timer to OFF, the circuit is OFF. http://waterheatertimer.org/Programmable.html#Aube
Plug-in-type timers have override button that turns programming off, and then you can operate table lamp normally with the lamp switch. But in that case, the lamp has separate switch that operates outside of timer functions.
GE 15070 24-hour mechanical timer could do what you want:http://waterheatertimer.org/images/GE-15070-mechanical-timer.jpg
In this specific case, when you wanted to operate timer like a light switch, you would move all the pins inward, and then use the on-off switch. The problem with this idea is the pins are tiny, and you need very good eyes or a light-source and small tool to continually adjust pins.
See GE timers and manuals:
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