Can you react to someone deploying a gear to a battlefield?

No — playing a gear is not something you get a reaction window to. Gear (and units) skip Step 2 Execute entirely: once the gear finalizes on the Chain it resolves immediately (Rule 337.2), so the state never stays Closed long enough for anyone to respond. Deploy changes nothing about this — it only changes where the gear may be played (Rule 830.1.b.1), not how it's played. So a deployed gear simply appears at that battlefield, and you're still in an Open State on their turn with nothing you can play.

What you can react to is any Play Effect the gear has ("When you play this…"). That trigger is placed on the Chain as a Pending Item after the gear enters (Rule 383.4.a.2), which closes the state and gives you a legitimate Reaction window — but you're answering the trigger, not the gear. And since triggered-ability targets lock at finalization (Rule 355.5.b), reacting won't let a newly revealed unit become its target.