In Swing you could set the blink rate of caret as:

JTextComponent c = new JTextArea();

// Set rate to blink once a second
c.getCaret().setBlinkRate(1000);

// Set the caret to stop blinking
c.getCaret().setBlinkRate(0);

But in JavaFX there are no available methods to set the blink rate of caret. It would be nice if there is a caretBlinkRate property which does this.