Even while using an image instead of a button or a div, the code and logic remains the same. Make use of the same Jquery function to navigate to the sheet you need. if you use the URL you are hard coding the to which sheet you are navigating. What if you happen to add a new sheet? Then your code will not work as it is not dynamic. So the kindly follow the way I have done in my extension to achieve what you need.
So here it is. I have created a sample navigation extension for you to refer to. This will help you build your extension.
I have placed this on sheet 4 of the app and can be used to navigate to next sheet, previous sheet or any other sheet based on its ID. I haven't created any customizing properties but you can add some for example : for a button you could have an input field to navigate to any sheet or URL, change text dynamically, change colors , layout options and stuff. As this is a sample I haven't spent enough time to do all of these.
Also, I have attached the zipped file of the extension for you to refer to. So Work away.