I know about the test gizmo that uses household
What do you refer to by this?

Concerning synchronisation there would be two ways:

-) modifying the contacts to make them close the moment the shutter is wide open (start of the 2nd curtain)

-) making an electronic device (maybe even in form of an external adaptor) that contains an electronic switch that is delayed by just that time the current synchronisation is in advance. Fine tuning could be done by experiment.