Can I trigger mobile menu via a different button?

I'm working on a site with a full width banner on the homepage. On all other pages, I've replaced navigation with the mobile menu (incl. desktop) and have a left-side logo in the header. I've successfully hidden the header on the homepage with the following in the page's header injection -

<style> 
  #header { 
    display: none;
  } 
</style>

and I've added a button in the top-right corner. Is it possible to use this button to trigger the mobile menu, either with a link or css? Or is there a better way to do this altogether?

Hi,

What is site url? We can check easier