I have some TextBox, when I hover my mouse over it, the cursor does not change:
However, when I enter some text, I do see a cursor when hovering:
I want the cursor to be visible in this text mode even when the textbox is empty.
The default behavior displays the I Beam when you mouse over a textbox, I'm unsure what is going on with your textbox, you may be overriding this behavior in a style.
You could implement this trigger to get around it:
<TextBox>
<TextBox.Style>
<Style TargetType="TextBox" BasedOn="{StaticResource {x:Type TextBox}}">
<Style.Triggers>
<Trigger Property="IsMouseOver" Value="True">
<Setter Property="Cursor" Value="IBeam"/>
</Trigger>
</Style.Triggers>
</Style>
</TextBox.Style>
</TextBox>