How to declare a click on a particular tab to be a new event for use with Rules?
Possible lead? The Rules Link module. The JavaScript option may be what you're after.
Here is a quote about it (from the module's project page):

... lets you create links which trigger arbitrary functionality with the help of Rules.
Example use cases:

Publish/Unpublish content
Subcribe users to current group
Mark nodes, comments (as Spam), unpublish it and block the author.
Batch functions like, delete all comment for a node

And many more...
Features:

Attach the link to any entities.
Show the link only for certain bundles.
Narrow the entities on which the link will be shown using the visibility conditions.
The links are usually displayed using Views.
For entities that can be displayed, the links can be shown on node view.
Supports an arbitrary number of additional Rules parameters for passing context via Views.
3 types of links: Javascript, Normal and Confirmation form links.
Use individual permissions for each link.

Usages:
There are three types of links:

Javascript - Links that will trigger the rules using Ajax.
Token - This are basic links, that will reload the page after calling them.
Confirmation link - Show a confirmation form before executing the rule.