You may target a tapped artifact with Rust Tick’s activated ability.

Rust Tick doesn’t track the artifact’s controller. If the affected artifact changes controllers, Rust Tick will prevent it from being untapped during its new controller’s untap step.

If you control both Rust Tick and the affected artifact, that artifact won’t untap during the untap step in which you choose to untap Rust Tick. (It will untap during your next one.)

If the affected artifact is untapped by some other spell or ability, Rust Tick’s effect will not end. If you keep Rust Tick tapped, and that artifact becomes tapped again, Rust Tick will continue to prevent it from being untapped during its controller’s untap step.

If Rust Tick untaps or leaves the battlefield, its effect will end. This has no immediate visible effect on the affected artifact. (It doesn’t untap immediately, for example.) The artifact will just untap as normal during its controller’s next untap step.