  Spin noise spectroscopy is emerging as a powerful technique for studying the
dynamics of various spin systems also beyond their thermal equilibrium and
linear response. Here, we study spin fluctuations of room-temperature neutral
atoms in a Bell-Bloom type magnetometer. Driven by indirect pumping and
undergoing a parametric excitation, this system is known to produce
noise-squeezing. Our measurements not only reveal a strong asymmetry in the
noise distribution of the atomic signal quadratures at the magnetic resonance,
but also provide insight into the mechanism behind its generation and
evolution. In particular, a structure in the spectrum is identified which
allows to investigate the main dependencies and the characteristic timescales
of the noise process. The results obtained are compatible with parametrically
induced noise squeezing. Notably, the noise spectrum provides information on
the spin dynamics even in regimes where the macroscopic atomic coherence is
lost, effectively enhancing the sensitivity of the measurements. Our work
promotes spin noise spectroscopy as a versatile technique for the study of
noise squeezing in a wide range of spin based magnetic sensors.
