jackstall To troubleshoot, Can you try add one of header content block from varied content block categories available and let us know as to how the menu module goes in responsive screen as I have tried adding the same and the toggle menu appears fine for menu module in responsive screen mode. Ref: Screenshot.
Varied content block options available for use can be referred from here
As apparently seen, The toggle menu functionality in responsive mode isnt extended currently to menu module assigned in spotlight content block types