In a previous article, 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 anticorrelation 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 ρ=−0.38+0.1−0.1ρ=−0.38−0.1+0.1 and p=0.15+0.14−0.09p=0.15−0.09+0.14. Adding three more GRBs to the sample, each with a pair of equally possible angle values, can strengthen the anticorrelation to ρ=−0.46+0.09−0.08ρ=−0.46−0.08+0.09 and p=0.05+0.07−0.03p=0.05−0.03+0.07. We show that these results are incompatible with non-stationary jets having Gaussian profiles, and that ≳100 GRBs with observed afterglows would be needed to confirm the potential existence of the angle-variability anticorrelation with 3σ significance. If the connection is real, GRB jet angles would be constrainable from prompt gamma light curves, without the need of afterglow observations.