Run this code -
import javafx.scene.control.*;

var tb: TextBox = TextBox {
columns: 10
text: "This is JavaFX"
}

You will see a textbox. Just click the textbox and make sure the caret blinks. Now press 'ENTER' key a couple of times. You will notice that the caret no longer blinks.

Reproduced on Soma-b25, WinVista.