Is the order of the events reversed here?
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Feb19-12, 05:55 AM
[..] one simple way is the observer at the source releases a light signal toward B to close it before starting the emission of lights toward A & B. And given his position in the train and the speed of light, he knows that B must be closed shortly after A
Yes, that should work.
Just a little remark, in view of your "knows [...] must": this time reversal is related to the way the one-speed of light is defined - and not really known - differently by the different observers.