This question is relatively obscure, so I don't think the solution will be generally applicable to anybody else. The basic solution is to use a Timeline to automate updating the selection in the ListView when the user presses a "Cycle" button in the UI.
There is a bit of additional logic to handle edge cases such as what to do if the user modifies the selection while the cycling is ongoing or if the user restarts the cycling process. If the user clicks on the currently selected item, the automated cycling does not stop, so the original asker might wish to add some of his own code to do that if he adopts a similar solution.
Also there is some logic for placing ImageViews in the ListView, but that isn't central to the application and can be ignored for more common types stored used in a ListView such as Strings. The ImageView related stuff is just there to make the app look a bit better.

import javafx.animation.*;
import javafx.application.Application;
import javafx.collections.*;
import javafx.geometry.Insets;
import javafx.scene.Scene;
import javafx.scene.control.*;
import javafx.scene.image.*;
import javafx.scene.layout.VBox;
import javafx.stage.Stage;
import javafx.util.Duration;
import java.util.Arrays;
import java.util.stream.Collectors;
public class RotatingSushiMenu extends Application {
private static final Duration AUTO_CHANGE_PAUSE = Duration.seconds(2);
private boolean autoChange;
@Override
public void start(Stage stage) {
ObservableList<Image> images = FXCollections.observableList(
Arrays.stream(IMAGE_LOCS)
.map(Image::new)
.collect(Collectors.toList())
);
ListView<Image> list = new ListView<>(FXCollections.observableList(images));
list.setCellFactory(param -> new ImageListCell());
Timeline timeline = new Timeline(
new KeyFrame(Duration.ZERO),
new KeyFrame(
AUTO_CHANGE_PAUSE,
e -> {
int curIdx = list.getSelectionModel().getSelectedIndex();
if (curIdx < list.getItems().size() - 1) {
autoChange = true;
list.scrollTo(curIdx + 1);
list.getSelectionModel().select(curIdx + 1);
autoChange = false;
}
}
)
);
timeline.setCycleCount(list.getItems().size());
Button cycle = new Button("Cycle");
cycle.setOnAction(event -> {
if (list.getItems().size() > 0) {
list.scrollTo(0);
list.getSelectionModel().select(0);
timeline.playFromStart();
}
});
list.getSelectionModel().getSelectedItems().addListener((ListChangeListener<Image>) c -> {
if (!autoChange) {
timeline.stop();
}
});
VBox layout = new VBox(10, cycle, list);
layout.setPadding(new Insets(10));
stage.setScene(new Scene(layout));
stage.show();
}
public static void main(String[] args) {
launch(args);
}
private class ImageListCell extends ListCell<Image> {
final ImageView imageView = new ImageView();
ImageListCell() {
setContentDisplay(ContentDisplay.GRAPHIC_ONLY);
}
@Override
protected void updateItem(Image item, boolean empty) {
super.updateItem(item, empty);
if (empty || item == null) {
imageView.setImage(null);
setText(null);
setGraphic(null);
}
imageView.setImage(item);
setGraphic(imageView);
}
}
// image license: linkware - backlink to http://www.fasticon.com
private static final String[] IMAGE_LOCS = {
"http://icons.iconarchive.com/icons/fasticon/fish-toys/128/Blue-Fish-icon.png",
"http://icons.iconarchive.com/icons/fasticon/fish-toys/128/Red-Fish-icon.png",
"http://icons.iconarchive.com/icons/fasticon/fish-toys/128/Yellow-Fish-icon.png",
"http://icons.iconarchive.com/icons/fasticon/fish-toys/128/Green-Fish-icon.png"
};
}