Run the attached test case. Note that after the test is complete the caret stops being updated. With fix for JDK-4512626 the caret stays non-blinking, without it the caret disappears. If you click a button and then click back to the textField causing the focus to change caret will start working as expected.

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import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JTextField;
import javax.swing.SwingUtilities;
import java.awt.BorderLayout;
import java.awt.Component;
import java.awt.Robot;
import java.lang.reflect.InvocationTargetException;

public class CaretThing {

    static JFrame frame;
    static JTextField textField;
    static Robot robot;
    static JButton button;

    static void printBlinkRate() {
        System.err.println("Caret blink rate: " + textField.getCaret().getBlinkRate());
    }

    static void requestFocus(Component component) throws InterruptedException, InvocationTargetException {
        robot.waitForIdle();
        robot.delay(300);

        SwingUtilities.invokeAndWait(() -> {
            System.err.println("Requesting focus on " + component);
            printBlinkRate();
            component.requestFocus();
            printBlinkRate();
        });
    }

    static void changeEditable() throws InterruptedException, InvocationTargetException {
        robot.waitForIdle();
        robot.delay(300);
        SwingUtilities.invokeAndWait(()-> {
            System.err.println("Changing editable");
            printBlinkRate();
            textField.setEditable(!textField.isEditable());
            printBlinkRate();
        });
    }

    public static void main(String[] args) throws Exception {
        robot = new Robot();
        robot.setAutoWaitForIdle(true);
        robot.setAutoDelay(50);

        SwingUtilities.invokeAndWait(() -> {
            frame = new JFrame("Hey");
            frame.setLocationRelativeTo(null);
            textField = new JTextField("Some long field value");

            textField.setEditable(false);
            frame.setLayout(new BorderLayout());
            frame.add(textField, BorderLayout.NORTH);

            button = new JButton("Button");
            button.addActionListener((e)-> printBlinkRate());

            frame.add(button, BorderLayout.CENTER);
            frame.pack();
            frame.setVisible(true);

            button.requestFocus();
            textField.getCaret().setBlinkRate(250);
        });

        requestFocus(textField);

// requestFocus(button); // comment this to get 0 blink rate on editable field

        changeEditable();

        requestFocus(textField);

        SwingUtilities.invokeAndWait(CaretThing::printBlinkRate);
    }
}