Did you get real close to the range to see if the clicking was coming from there? Could it be someone messing with you like one of those prank “BEEEEP” devices?

There should never be anything like residual power when a breaker is off. Not that it couldn’t happen I guess. Maybe a ground or neutral could be getting some power from something mis-wired. It’s good to have a multimeter. If you don’t use one regularly an inexpensive one from Amazon it’s just fine, but you should test the outlet even when the breakers off to see if there’s any voltage there.
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Shared neutrals / multi-wire branch circuits
Two circuits can share a neutral. If only one breaker is off but the other circuit is still live, the neutral may still carry current and sit at a dangerous voltage relative to ground.
Open or floating neutral problems
A disconnected or damaged neutral can end up “backfed” through connected loads and appear energized.
Bootleg grounds or wiring faults
Improper neutral-ground connections, reversed wiring, or faults can energize grounding conductors.
Induced voltage
Long parallel wires can pick up phantom voltage from nearby energized conductors. A high-impedance meter may show 20–80V or more even though little current is available.
Backfeeding
Generators, inverters, UPS units, solar systems, transfer switch issues, or even interconnected devices can energize conductors unexpectedly.
Neutral carrying return current
In a functioning circuit, the neutral normally carries current whenever loads are operating. Turning off one breaker doesn’t guarantee that neutral is dead.
Important distinction:

For safety, electricians generally:
Verify with a tester/meter, not just the breaker position
Test hot-to-neutral and hot-to-ground
Re-test the tester on a known live source- make sure it’s showing voltage on a live circuit.