Since the caret is shown, but not blinking, then I am guessing your control has Logical Focus, but not Keyboard Focus.
How are you setting the control as Focused?
myControl.Focus();
will give the control logical focus, but it won't respond to keyboard events because it doesn't have Keyboard focus. To give an element KeyboardFocus, use
Keyboard.Focus(myControl);
This is because WPF allows you to define multiple Focus Scopes, and each scope can have it's own focused element, however only one control in the entire application can have Keyboard Focus
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