A simple lab timer or special application type timer switch. Article, said 2 to 20 second timer. Multiple contacts could be used for different turn- on times. Videos shows this could be much longer times,
At the top, drops of mercury are falling into empty catch tube at steady rate. As this tube fills to open switch level inside tube, ( close switch), an electrical circuit is made through the mercury.
Mercury can still be bought in United States. It is hazardous material and not a good idea to have large amount in a home. Safe handling practices have to be done if large amount.
A regular mercury switch circuit from thermostat could be set to tilt as bucket fills\ leaks empty either water or sand in basic experiment application.