Hide the cursor not the mouse pointer

Question

I have a TextBox and a button: button_InputComplete. When I finished inputting the data in the TextBox I press the button and the button_Click event handler is invoked.
While the button_Click event handler is executing there remains a cursor in the TextBox at the end of the input data (a vertical blinking line).
I would like to hide this cursor. I do not mean the mouse pointer but the cursor in the TextBox (the vertical blinking line). I also need to be able to restore it.
The Cursor.Hide() statement hides the mouse pointer.
I tried to move the focus away from the TextBox with the statement: this.Select(); but the cursor remained in the TextBox.
I also tried the statement: control.Select(); where control is an instance of another control located on the form (not the TextBox), but neither this worked (the cursor remained in the TextBox).
Any help with an idea would be greatly appreciated.
Thank you in advance.