Who IS Cait Sith?

In Final Fantasy VII it's revealed Cait Sith is actually

a robot controlled by someone in Shinra Headquarters.

As you've been there before, is there any clue to whom it actually is at any point?

In Final Fantasy VII Cait Sith is a cat, riding a giant stuffed toy moogle, working as a fortune-teller in the Gold Saucer. His true identity is that of Reeve Tuesti's who controls Cait Sith remotely like a puppet. Even though Reeve is Shinra Electric Power Company's head of Urban Development he is interested in saving the Planet.

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Reeve is an Architect who designed the Mako reactors. He supports the cancellation of the Space Program following the crash in Rocket Town. He later supports the Turks when they briefly split from Shinra by using his puppet, Cait Sith to aid them.

The character of Cait Sith actually appears in several other entries in the Final Fantasy series, usually as just a cat, sometimes as a summon other times as an enemy.

Source Final Fantasy Wiki

If I remember correctly, there is a bit of dialogue where Barret identifies Cait Sith's true identity when he says something like

You're caught Reeve.

I believe there are a few other hints dropped, but it has been a while since I played through FF7