Since this appears to be a non-issue, for others, I will report on how things have progressed.
Some link open the browser, but others try, always, unsuccessfully, to open a new Tab in TB3.6.12. For those link, I right click|open in browser, and everything is ok. I don't know why this is happening, but since it never happened with TB2.x, it must be something about 3.x.
I added an "etc." to the subject, because, I might as well complain about 3.6.12, which I, thoroughly, dislike.
The propensity of opening Tabs is a gripe. For instance, I have the Webmail notifier addon, which allows to get Webmails, like Yahoo, and Gmail. The settings are to open the Webmail in another Tab. This is fine, except, that I can't see any way to open two accounts in two separate Tabs. But, if mail is removed to Trash, a separate Tab opens, and it is, then possible to open the other account in that Tab. But if TB is closed, and Tabs are left, an identical copy of the default account opens in a third Tab. Of course, it must be a defect of the addon, but why are Tabs there, if they cannot be controlled, like in Firefox.
If one knows how to control the Tabs, please, point me in the right direction.
UserAgent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.9.2.12) Gecko/20101026 Firefox/3.6.12