What are the guidelines for constructing variable names that follow CF conventions?
Possible this is not what you need, but here's an archive of the Guidelines for Construction of CF Standard Names, which is "Version 1, 3 December 2008" and was cached on July 28, 2013; guessing that the page has not been updated since December 2008.

Also, the source code repository for CF Conventions website you linked to (cf-convention.github.io) is viewable from here; if you had questions about the status of the site, you might try contacting the developer listed on Github for the project; their email is listed on their Github profile.

UPDATE: Here's the contact info for the CEDA Data Scientist; their "main role in CEDA is the development of metadata standards, particularly the CF (Climate and Forecast) metadata conventions."