Using RTC DS3231 + Arduino UNO to calculate time lapsed
One idea would be to use force/pressure sensor on chair. You have to find what the sensor outputs when an average person sits on it and calibrate the values accordingly in code. Finally you have to a set threshold value for it. Now if somebody sits on it and if that threshold is exceeded, it means somebody sat on it. So you can now trigger your rtc module or maybe you can use special peripherals called timers , which are inside arduino itself. Both can be used to keep track of time. Tutorials are available for both timers, and ds3231- arduino interfacing. You can easily code. Good luck :-)