I went ahead and added a disconnected frame of page-type "Right" after the Left I was working on, and clicked one frame and then the other, and joined them by using Format > Customize Layout > Connect Text Frames. It seemed to work, but text still does not flow from the first to the second. I tried to connect them a second time, and FM says they're already connected. WHY NO FLOW? Thanks in advance.
A possibility is that what you inherited is not using default Left/Right MPs, but MPs with other custom names, and those MPs have flow issues.
Check the MP assignment. See if there's a Reference Page named MasterPageMaps, and what tags are mapped to what.
Believe it or not I tracked the problem down to a corrupted footnote. No point in explaining ... it's fixed.