There are some circuit ideas here and here for generating a shorter pulse from a longer one.
However, they are intricate enough that if I were trying to do it, I'd just use an Arduino microcontroller to detect the SC2 signal and trigger your device for whatever time period you need. You can get small US-sourced Arduinos for $5; less from China.
Depending on how your momentary button is wired, the Arduino might be able to trigger it on its own; otherwise the Arduino could close a relay that would trigger your device.
if you have a DZ-2001 data wire driver the Arduino could even read a command over the serial line directly without involving the SC-2, but that's a little more complicated programming.
