Is it possible (and how) to create a conditional text based on whether the page is odd or even?
Insert > Field > More Fields > Functions > Conditional text > … but what next?
note: This is not for running headers. This should be in the main area of a page and not in the header.
Very good of you to distinguish that this was not a header footer question. Can you go a step further? What kind of boiler plating are you looking for? Would a macro solution be a possibility, or are you specifically asking about the capabilities of conditional text in a field?
A macro would be an overhead, “too much”. I need this for just two specific pages in the middle of a document, and in case it won’t be possible with a conditional text, I would prefer to maintain these “captions” manually.
Since you need this only for 2 specific occurrences, could you describe more precisely the use case? Maybe conditional text is not the way to go. Perhaps a constrained page style could do the job. Tell exactly what you want in these pages. What is the relationship with preceding/following pages? Continuity or inserted blank page allowed?
This is actually for the template and the page styles are already assigned. I cannot add any kind of “tricks” to the page styles, since this will in fact harm the template 
Well, it seems the best option is to maintain these captions manually.
Attach the template. I’m very curious about what you’ve already done.