  Among the properties shaping the light of a galaxy, the star formation
history (SFH) is one of the most challenging to model due to the variety of
correlated physical processes regulating star formation. In this work, we
leverage the stellar population synthesis model FSPS, together with SFHs
predicted by the hydrodynamical simulation IllustrisTNG and the empirical model
UNIVERSEMACHINE, to study the impact of star formation variability on galaxy
colours. We start by introducing a model-independent metric to quantify the
burstiness of a galaxy formation model, and we use this metric to demonstrate
that UNIVERSEMACHINE predicts SFHs with more burstiness relative to
IllustrisTNG. Using this metric and principal component analysis, we construct
families of SFH models with adjustable variability, and we show that the
precision of broad-band optical and near-infrared colours degrades as the level
of unresolved short-term variability increases. We use the same technique to
demonstrate that variability in metallicity and dust attenuation presents a
practically negligible impact on colours relative to star formation
variability. We additionally provide a model-independent fitting function
capturing how the level of unresolved star formation variability translates
into imprecision in predictions for galaxy colours; our fitting function can be
used to determine the minimal SFH model that reproduces colours with some
target precision. Finally, we show that modelling the colours of individual
galaxies with percent-level precision demands resorting to complex SFH models,
while producing precise colours for galaxy populations can be achieved using
models with just a few degrees of freedom.
