Common mistake. You have set the Border.Background property directly which will always override the value set by your trigger. (Locally set values have a very high precedence, style has a pretty low precedence.)
Instead, you should move your “normal” background into the Style like so:
<Border>
<Border.Style>
<Style TargetType="Border">
<Setter Property="Background">
<Setter.Value>
<LinearGradientBrush>
<LinearGradientBrush.GradientStops>
<GradientStop Color="Aquamarine" Offset="0"/>
</LinearGradientBrush.GradientStops>
</LinearGradientBrush>
</Setter.Value>
</Setter>
<Style.Triggers>
<!-- the trigger you showed -->
</Style.Triggers>
</Style>
</Border.Style>
</Border>