Testing Long Time Delay
Power a mechanical clock with the output of the timer. Either a mains clock, or one of these one AA battery cheap clock movements that turn up everywhere, depending on what your test system switches.

Set the test clock to 12:00, record the time you set the timer going. You only need to make three more visits to the test setup, and their times are fairly flexible. Make the first visit before 21 hours, to check the test clock still shows 12:00. Visit between 21 and 24 hours after starting, to check that the test clock is running, and that the time shown indicates that it started when expected. Make the next visit some time between 24 and 45 hours, to make sure that it is stopped, showing a time of 03:00.

If you want documentary evidence of the test working, photograph the test clock next to a normally running time and date clock, and annotate the print by hand to explain what can be concluded from the times.

If you put the test away in a cupboard for a week, then when you come back, the test clock should have advanced 3 hours per day of the test.