How can I be alert when it matters and calm the rest of the time?

You have described the ideal of your whole trade, the calm guardian. Alert when it matters, at rest when it does not. That is not a lucky temperament. It is a skill, and the fact that you can name it means you are already reaching for it. The strongest protectors are not the most tense. They are the most settled, because a settled mind sees clearly and acts without panic. The key is trusting your own alarm. A guardian who is always braced does not actually trust himself to notice trouble, so he tries to notice everything at once and exhausts himself. A calm one trusts that when something real appears, he will snap to it. That trust is what lets him rest in between. Your alertness is not weakened by your calm. It is sharpened by it, held in reserve for the moment that needs it. So build both halves on purpose. Train the alertness, yes, but also train the rest, because the rest is what most people neglect. On a quiet watch, let your body ease while your attention stays open, and remind yourself you will rise to what matters when it comes. Alert when it counts, calm when it does not. That balance is the whole art of the guardian, and it is learnable.