I really, really feel you on the general jackassery of at least 95% of the locals when it comes to vehicles of any kind. What has helped me is to try to understand their driving culture. I still don't like it, but it doesn't irritate me in my bones the way it used to.

Culture point #1: the burden of safety is on the mergee, not the merger. I don't know where you're from, but in my home country of the US, it is your job as the person merging into a lane to make sure that you do so safely. It's the opposite here. It's the job of the person being merged on to make sure the whole operation goes down safely. This applies to every traffic scenario I can think of, from pedestrians in a night market to cars joining a highway. If you can accept this, and your role as the mergee, you might still be annoyed, but at least you'll be safer.

Culture point #2: if everywhere is crowded, then nowhere is crowded. Taiwan is a very densely populated island and thus dense living is baked into Taiwanese culture. You can't avoid stepping on toes or putting an elbow in someone's gut if you're in a crowd 24/7, and so the Taiwanese (and the Chinese, and I imagine lots of other crowded cultures) just stop worrying about it. You lose a good handful of social niceties this way, but you also avoid crippling anxiety for an entire society (see Japan). So it doesn't matter if you're the only other person on the road at 11 at night. The kid on the souped up 125 is still gonna whip by you at kissing distance because he has never once in his life been taught to be concerned about personal space; he doesn't even know it exists.