Optical colour variability and inter-band timing probe synchrotron evolution in blazar jets, but survey cadence can bias colour–magnitude trends and apparent lags when multi-band sampling is non-simultaneous and interrupted by seasonal gaps. We analyse Zwicky Transient Facility (ZTF) $g$ - and $r$ -band photometry of the high-synchrotron-peaked blazar 4FGL J0540.5+5823. Quasi-simultaneous colours are constructed by nearest-neighbour pairing within $\Delta t_{\max }=0.03-0.05$ d, and two-band activity episodes are defined objectively via Bayesian Blocks restricted to the $g/r$ overlap. Colour–magnitude slopes are measured with robust regression, and their significance is assessed with a season-wise block-permutation test to account for clustered cadence. Inter-band delays are estimated with the z-transformed discrete correlation function (ZDCF) and, for the three best-sampled episodes, with flare peak-time offsets from asymmetric envelope fits. We find a persistent bluer-when-brighter trend ( $b=0.063\pm 0.013$ for $\Delta t_{\max }=0.05$ d) with sampling-aware significance $p_{\mathrm{block}}=6.3\times 10^{-3}$ . The global ZDCF prefers a positive lag of order 10 d but with broad uncertainty, while episode-level ZDCF lags are consistent with zero; envelope fits reveal one episode with an $r$ -leading peak offset of $8.2\pm 2.2$ d. The coexistence of a stable baseline colour trend with episode-dependent timing behaviour favours band-dependent profile evolution rather than a rigid inter-band delay, motivating denser multi-band and polarimetric follow-up.
