Many cameras have a 2 step shutter release. A "half press" wakes the camera up, activates automatic focusing, etc, and a "full press" then activated the shutter release (when the camera is ready).
To minimise shutter lag (the wait for the camera to be ready), you need to give sufficient time between the "half" and "full" press. In circuits I've made, I have activated the "half press" up to a second before the "full press".
If you want to take shots **NOW** then you might even have to leave the "half press" activated constantly (this may be the easiest).
Some cameras allow you to only close the "full press" contacts, but others require the "half press" ones to be closed as well. You discover this by experimenting
So, your sensor would complete the "full press" circuit, and you would either a) leave the other pair unconnected, b) leave the other pair shorted, c) switch both pairs together (you may require diodes), or d) need to do something more clever.
Sorry, I thought you had 2 of the same cameras. It would be easier to give the make and model numbers rather than their attributes too.