If you want to preserve what's already been painted so that you get a trail of red ovals instead of a single red oval as the mouse moves, then you shouldn't paint directly on the Graphics object provided by paint(). Instead, use a BufferedImage to store your state. Then render the BufferedImage onto the Graphic provided by paint().
private BufferedImage image = new BufferedImage(width, height, BufferedImage.TYPE_INT_RGB);
public void paint(Graphics g) {
super.paint(g);
Graphics imageGraphics = image.getGraphics();
imageGraphics.setColor(Color.red);
imageGraphics.fillOval(mouseLocX,mouseLocY,30,30);
g.drawImage(image, 0, 0, null);
}
The BufferedImage provides the persistence for the previous draw operations.