When Covert Operative comes on board, choose an engine your opponent controls. Exhaust it if it is ready. It doesn't ready in their next stoke phase.
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Explained
When Covert Operative comes on board, choose an engine your opponent controls. Exhaust it if it is ready. It doesn't ready in their next stoke phase.301.10
Not when you deploy it: it happens once it has resolved and is on board, after your opponent's chance to react. Put on board without being deployed, as by Resurface, it happens too. In the sortie phase it goes into the crossfire (301.10). Choose one of your opponent's engines when it happens, ready or exhausted; with only one, it is chosen, and with none, nothing happens. It stays exhausted through their next stoke phase, so they lose its steam until the one after (801.14).