The "problem" might be with both accordions, they do not close, once users have clicked, if everything is on the same page.
If the corresponding menu item leads always to a new page then it will work with the accordion out of the box.
Try it this way:
Place the accordion not on your master, but one (the same) on every single page.
Open on that page the appropriate tab of the accordion.
Link the accordion’s title bars on every page to their respective pages.
You may download the respective .muse file directly from this site.
Thanks Gunter! This was a way I was thinking but wasn't sure if there was any others! Helped so much.
It is not THAT elegant and streamlined, but it works after all!