A Basic Angle (BA) of 106.5° separates the view directions of Gaia's two fields of view (FoV). A precise determination of the BA variations (BAV) is essential to guarantee a correct reconstruction of the global astrometric sphere, as residual systematic errors would result in, e.g., a bias in the parallaxes of the final Gaia catalog. The Basic Angle Monitoring (BAM) device, which provides a reliable and accurate estimation of BAV, shows that there exists a ~1 mas amplitude, 6-h period BA oscillation. It's essential to verify to what extent this signal is caused by real BAV, or is at least in part an effect of the BAM device itself. Here, we propose an astrometric on-sky approach to re-determine the 6-h periodic BAV. The results of this experiment, which treated a full day (17 Oct 2016) of Gaia astrometric data, recover a value for the 6-h oscillation of 1.856±0.857 mas. This is consistent, within the errors, with the BAM finding for that day.