Well, you could signal that by failing to renew the canary on schedule. Once there's a gag order, no signaling takes place. There's no "removal".

Right, another name for a canary is a heartbeat, which are used in systems to know if a system is still up:

https://en.m.wikipedia.org/wiki/Heartbeat_(computing)

Right, exactly. A heartbeat. And further, the signing key could be deleted securely, so coercion or spoofing would be impossible. That, however, would be an argumentally illegal action taken after the gag order. One could have an anonymous third party responsible for that. But then they have much power. And the signal to them would also be an argumentally illegal action taken after the gag order.

This is pure speculation/assumption, but I'm guessing it's because the government can't compel someone to lie, or something like that. I have no citations for this, though... It's just what I always assumed when I heard about canaries.

If, on the other hand, the government is allowed to compel someone to lie, I'd really like to know more about that...