Trolling is absolutely a form of bad faith communication. However, you needn't look far on twitter to find that trolls are pretty high hanging fruit compared to ideological flamewars perpetuated by non-trolls fighting to score points for their respective ideological teams.
Upon further reflection, I realize that there are many "true believers" of one sort or another who aren't trolling but whose minds are completely closed and aren't looking for good faith dialogue but to proselytize their belief or attack those of their opponents.
Trolling often involves bad faith communication, but bad faith communication isn't necessarily trolling. Consider politicians, salespeople, and advertisers who are willing to convince by any means possible.
"Plain old trolling" in the traditional sense (e.g. back with newsgroups) is seeking to provoke an emotional reaction, but without regard to the truth of falsity of the statement, and not necessarily with any grander agenda.
It was only later that it came to be (mis?)applied toward organized disinformation campaigns.
Because "bad faith communication" is about the talking head on the TV sowing doubt in your mind on complex issues. It is oil company shills telling you that climate change is not man made and it is Malthusian environmental activist that it is impossible to get safe and carbonfree energy from nuclear. Neither of these are communicating with you in good faith because they have an agenda.
By strict definition it is bad faith because the troll's goal is agnostic to the position advertised and the only real intention is to provoke people.
However I think that like art, trolls can use a lie to tell the truth. My preferred example is James Randi (https://en.wikipedia.org/wiki/James_Randi, see also the documentary An Honest Liar). You might say that his goal was not to provoke a reaction, but given the repeated humiliations of the conman he exposed I beg to differ.
Personally I like to tell the exact opposite of the truth that nobody knows or most people ignore but would make them change their mind. For instance, it is known vaccines are used to only prevent hospitalizations.
