Well now that we found out what was the problem.
How about you stop using empty images for the future and instead you use Rectangle:
<DockPanel HorizontalAlignment="Stretch" Name="dpDirectorImg" VerticalAlignment="Stretch" Grid.Column="1" Grid.Row="8">
<Rectangle MouseDown="imgDirectorSignature_MouseDown" />
</DockPanel>
If the rectangle has any background color by default you can change it to transparent
Background = Transparent
Glad I was able to help you out on this and notice, when Background or Source of an Image is NULL, the hit testing in wpf will not work. That is by design.
Set Background to transparent or any color you like :)