If you use the Custom Google Search option with the results on a separate page, you will get a second copy of the search results in the footer, if the search box is placed in a footer widget area. I could grant support access, but it's just a plain sandbox site with nothing on it. Testing will also require access to your own Google CSE dashboard. Here is the detailed testing scenario.
WordPress theme: Twenty Seventeen
All plugins disabled except WPMUDEV Custom Google Search
Place WPMUDEV Custom Google Search widget in footer widget area
Google CSE control panel
- Look and feel > Layout: Two page
WP Dashboard > Settings > Custom Google Search
- Embed Code: search box code from Google CSE control panel
- Display search results as: Custom Page
- Search Results Page: Search Results
Create a page called "Search Results"
Paste as plain text the Search Results code from Google CSE control panel