Hmmm... must be the starting position. There is one chain which either resets them all or opens the portcullis. If you go back and forth as I described, eventually (and without taking too long) it's the only one up.
A specific pattern like you posted is probably better and faster... only I can never remember what it is, so I have to go searching through my notes, so...
Ah, well. There are many ways to play the game, for sure