I take it then that you do not actually wish the text in the textbox to be selected, as the behavior of the cursor with regard to selected text is plaform- and browser- dependant. So just change the background and text color of the textbox:
var textbox = document.getElementById("textbox");
textbox.style.backgroundColor = "blue";
textbox.style.color = "white";
...etc.
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You're right. These facts that you've laid out totally contradict the wild ramblings that I pulled off the back of cornflakes packets.
