To continue ambiguously arguing your point even though you know you are incorrect (i.e. flat out wrong) and your opponent has even shown this in great detail (but you are somewhat sure the audience can't tell the difference). This is a great time to practice strawman arguments or simply let loose a deluge of ad hominem attacks.
Internet chat and bulletin boards have been excellent breeding grounds for tergiversation as people no longer have to worry about losing their integrity to such displays and the intelligence of the audience is completely ambiguous.
Randroids, in particular, are quite familiar with the technique and it is the main argumentative tool use to rationalize her many political and philosophical contradictions.
Tergiversation is a five star trolling technique if you maintain even a slightly above average vocabulary.
The tergiversation of Ayn Rand's speech left her listeners confused about where she really stood on the issue.