The only flight controls we see are an array of stay-state toggle switches (see the lower right hand of the image above) and banks of lights. It’s a terrifying thought that anyone would have to fly a spaceship with binary controls, but we have some evidence that there’s analog controls, when Luke moves his arms after the Falcon fires shots across his bow.
Unfortunately we never get a clear view of the full breadth of the cockpit, so it’s really hard to do a proper analysis. Ships in the Holiday Special appear to be based on scenes from A New Hope, but we don’t see the inside of a Y-Wing in that movie. It seems to be inspired by the Falcon. Take a look at the upper right hand corner of the image below.