  We investigate a disorder-free quantum Ising chain subject to a time-periodic
drive that rotates each spin by an angle $\pi(1-\epsilon_i)$. In case all spins
experience the same deviation $\epsilon$ and the system is initialized in a
fully polarized state, the dynamics is known to be time-crystalline: the
magnetization of the system exhibits period-doubled oscillations for timescales
that grow exponentially with the length of the chain. In this work, we study
the effect of a deviation $\epsilon$ that differs between spins. We find that
reducing $\epsilon$ for a single spin drastically enhances the lifetime of
spatio-temporal order, suggesting the name ``metronome" spin. Employing
perturbative arguments in an average Hamiltonian picture, we explain this
observation for initial states with macroscopic bulk magnetization.
Furthermore, in the case of random bitstring initial states, we report the
enhancement of the lifetime of a topological edge mode, which can also be
understood in the same picture. Finally, we discuss an altered geometry in
which the metronome spin is not directly part of the chain, affecting the
dynamics in different ways in the two scenarios considered. Our findings unveil
the intricate dynamics that emerge in Floquet systems under the influence of a
spatially varying drive, thereby uncovering new avenues for Floquet
engineering.
