Predicted per-epoch centroid positions for J1058+0133 (left) and J1824+5651 (right), illustrating the signal expected from Gaia DR4 per-epoch astrometry. Top: Gaia light curves analogous to the left panels of Figure 3, with the linear trend in inverse flux. Bottom panels: centroid position along the jet predicted at each photometric epoch (black points) compared with the DR3 linear proper motion (blue line). The epoch-by-epoch excursions—driven by flux variability—illustrate the underlying signal that DR4 per-epoch astrometry will probe. Uncertainties of individual Gaia measurements are expected to be comparable to these excursions, implying that the correlation signal will only be visible in the aggregate.