The mobile hamburger menu of the Shopify theme "Dawn" does not have any block elements that can be added to the space below the menu list, so here is a setting example that uses a customized Liquid section and Javascript to display any HTML.
An example of how to display any HTML in the space below the menu list in the mobile hamburger menu of the "Dawn" theme (when using customized Liquid in the theme editor)

[Setup Method 1] Add a "Customized Liquid" section to the header group and insert the code

[Setting method 2] If you want to display it before the menu list, rewrite part of the code

