I tried to set the following in my css file :

.tab-pane *.tab-header-background {
    -fx-outer-border: #636363;
    -fx-inner-border: linear (0%,0%) to (0%,100%)
        stops (0%,ladder -fx-color
                      stops (0%,#F4F4F4)
                            (100%,#F4F4F4))
              (100%,ladder -fx-color
                      stops (10%,derive(-fx-color,20%))
                            (80%,derive(-fx-color,-10%)));
    -fx-body-color: #C0C0C0;
    -fx-background-color: -fx-outer-border, -fx-inner-border, -fx-body-color;
}

I do the same setting for .tab

While Tabs are updated using the 3 specified colors, the tab header seems to use only the -fx-body-color.

Attached the result of the above css setting vs the wanted rendering.