X-Y chart views (such as Line Chart View and Quartile Chart View) have the ability to show a green vertical line indicating the current time. You can hide this line (with the Hide Time Marker property), but you cannot otherwise change its properties such as color, thickness, and stipple. You should be able to modify its display.
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Written up here: https://gitlab.kitware.com/paraview/paraview/-/issues/22198. Funded, but no priority until I hear a user ask for it.