You need to plug the footswitch into the outlet at the back of the ST450 into the connector marked 'START'. You can plug a second footswitch into the 'FOCUS' connector.
It looks like it uses 'Jones' plugs. It is highly likely a Beseler footswitch would work. The timer wasn't designed by Durst but by EPOI in the US, and they designed it for a standard US footswitch.
As to using an external timer with these two boxes, I take it you would want to retain the stabilizer feature of the ST450. I think it would be possible, but to answer that definitively I would have to see how the two boxes attach to each other.