Considering “PointSize[0]” and even $[-1]$ in NumberLinePlot, why those circles still exist?

In this code, I put "PointSize[0]" (or [-1])

NumberLinePlot[{Sin[x] < 0, Sin[x] >= 0}, {x, 0, 13},   PlotStyle -> {Directive[Thickness[0.001], Red, CapForm["Butt"],      PointSize[0]],     Directive[Thickness[0.001], CapForm["Butt"], Black, Opacity[100],      PointSize[0]]}]

but I get this plot

enter image description here

As can be seen, those circles still exist (cf. magnified part). How can I get rid of these circles and have only line segments?