The clocks need precise oscillations to measure time: the mechanical clocks used pendulums and springs; the maser clocks used precise microwave cavities; the atomic clocks that are dominating today use oscillations of electrons in selected atoms.

Americium is not a good atomic clock material---it doesn't have superior electronic transitions, and the nuclear transitions causing its radioactivity would get in the way.

Nuclear oscillations could also be used: there is a proposal to use a low-energy nuclear oscillation in Thorium; it would be more stable than electronic oscillations: https://en.wikipedia.org/wiki/Nuclear_clock

The distinction of what can or cannot be called 'radioactive' is somehow artificial: masers, atoms and nuclei all emit radiation, so they all are technically 'radioactive'. Conventionally, 'radioactive' radiation requires energies that cause ionization of common materials, usually quoted as above 10eV. The Thorium nuclear transition is actually below that, so technically it is not radioactive---but I'd still not want to sit next to such clock without some shielding, because even UV radiation with energies above 3eV is known to damage living tissue.