I haven't attempted it yet, but I would probably use a short insulated rail on each of the switch legs and a relay to throw the switch machine. If I remember correctly, the LGB switch machine is activated by a momentary switch. My only concern is what happens when the relay sends repeated triggers to the switch machine with a long train.
Gunrunnerjohn is going to be making some great insulated rail relays, which are being discussed in another thread. I will use those, since many of my SG engines are MTH DCS.