If I understand your question correctly, you want to define a style for ToolTip
within your ToggleButton
.
Try this:
<ToggleButton Content="ON" Grid.Row="1" ToolTip="{Binding ElementName=tbText, Path=Text}">
<ToggleButton.Resources>
<Style TargetType="ToolTip" BasedOn="{StaticResource {x:Type ToolTip}}">
<Setter Property="Background" Value="Red" />
</Style>
</ToggleButton.Resources>
</ToggleButton>