When to tap Enkil Cog

Ok. Clear - thanks for that.
I admit, this opens it up for quite an interesting trick: asking for impulse, receiving it (before A completes his/her turn), B declining to take an action (passing), and so getting minion phase come to an end (so impulse doesn't go back to A, yet B still able to use EC at a later player's turn...)
Point taken.

If your trick aims at the idea that C would be "quicker" than B, I'd say this should only lead to a rollback. B would actively need to say "I pass" before C would get the impulse.

Rules-wise you can't force-skip B's declaration imo.