Now I'm wondering if you turn the stopwatch on, if it stores the time it turned on, or if it maintains the 'elapsed seconds'.
Could be testable by turning the stopwatch on and then change the time. I have no idea how these clocks work; if they have a Unix time style counter as internal reference, then this test won't work. Would need a 36 bit memory to run for 20 years continuous counting; 30 billion times bit flipping on the lowest bit. Probably done differently.