The site seems to work as designed only when the “mobile theme” as selected in the Plug-In settings is the designated “active theme” from the site dashboard. Specifically – I use a Child 2010 theme for desktop, and decided to use Twenty-Fifteen (which I will refer to as 2015) for the mobile. I customized the 2015 theme with different background colors and added a header image. To save the 2015 theme changes, I have to click “Save and Activate” in my theme customizer screen. OK, so I do that. If I then immediately check my Android mobile device running Firefox Beta, the mobile page behaves properly — the header image is displayed and the sidebar/content toggle button works. But then my desktop site shows the 2015 theme. If I change my main-dashboard theme selection back to Child 2010, my desktop goes back to the way it should, but now the mobile device does not show the header image anymore, and the sidebar/content toggle button does nothing (it is displayed but does not do anything). Furthermore, on the mobile device, my site name is displayed instead of header image, even though I have unchecked the box to display header site name and tag line. I can say that the Mobile Theme Switcher *partly* works because it does flow the text differently and is not simply a replica of the desktop page.
Yes, I have cleared the history and cache on the mobile and desktop browsers and disabled ad-block add-on to make sure nothing was stale, or interfering. Also, I see the same behavior on Firefox and Chrome. I am tempted to uninstall the Theme Switcher plugin, remove the files, reinstall and start over, unless you have a better idea. Thanks.