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However it might be a starting point for further work. I also did not find formal specifications for wikitext so it was a lot of learning by doing. However I used it successfully on ~4k "Infobox Chemie" templates in the de-wiki.
As far as I can see there is no such specification. We all know how the wikipedia handles text markup and what format we have to use (e.g. to create a heading and so on...) IF we use correct syntax...
The problem is what happens IF your use NON-VALID wiki syntax on a page? The mediawiki software will then do "something" to get (at least) a valid HTML page, but what fall-backs are used? How is the proirity when parsing and so on... In my opinion this is the main issue here since "our" wikitext parser should behave similar on wrong wiki syntax also... (quite a messy thing I experienced... obviousely I am not a parser expert too... ;)
This is why I did not write a parser just my tiny (holy) 'getSections' method.
Greetings DrTrigon