  In Budai et al. (2020) we argued that angular non-stationarities of gamma-ray
burst (GRB) jets can result in a statistical connection between the angle
values deduced from jet break times and the variabilities of prompt light
curves. The connection should be an anti-correlation if luminosity densities of
jets follow a power-law or a uniform profile, and a correlation if they have a
Gaussian profile. In this follow-up paper, we search for the connection by
measuring Spearman's rank correlation coefficient in a sample of 19 long GRBs
observed by the Swift satellite. Using 16 of the GRBs with well-defined angle
measurements, we find $\rho = -0.20_{-0.09}^{+0.09}$ and $p =
0.46_{-0.19}^{+0.23}$. Adding three more GRBs to the sample, each with a pair
of equally possible angle values, can strengthen the anti-correlation to
$\rho=-0.31_{-0.08}^{+0.07}$ and $p=0.19_{-0.09}^{+0.14}$. We show that these
results are incompatible with non-stationary jets having Gaussian profiles, and
that $\gtrsim\!100$ GRBs with observed afterglows would be needed to confirm
the potential existence of the angle-variability anti-correlation with
$3\sigma$ significance. If the connection is real, GRB jet angles would be
constrainable from prompt gamma light curves, without the need of afterglow
observations.
