A lot of good stuff has been written already, especially about second tier cities (or even the countryside).
I would also recommend avoiding other English teachers for the reasons mentioned above. Even aside from the fact that the industry is full of drunks and other assorted misfits, ESL in Asia is where dreams come to die. It's full of people with zero ambition in life. That can provide opportunities though if you're not like that. The trick is not becoming like that without realising it.
I'll just throw in a few expansions on some of the points that have already been made.
Private lessons are pretty common in Taiwan. It's also a far less xenophobic country than Korea based upon all the people I have known who have lived in both.
The trouble with private lessons is that, as with English teaching generally, the market is completely saturated unless you live outside a large metropolitan area or you're willing to do something different. Every single other sociology major from a state university in the US, plus seemingly half of Canada and South Africa, has already thought of coming here to pay off student debt. There's a bit of a race to the bottom with private tutoring in Taiwan or with the industry in general. I have known people here who have saved crazy money in a very short time, but that can be pretty difficult if you need to get your visa through your job. The cram school industry here is notoriously exploitative. It's also full of enablers: fat South African chicks who don't have boyfriends and will never get boyfriends. Bosses here are aware of this, even if only at an instinctual level, and they are also aware that said women cannot/will not leave Taiwan. Therefore, if they want someone to make posters on a Saturday night at home, there will be lots of willing victims. Compared to such people you can only ever look like a bad employee and so will have to endure massive amounts of bullshit as a result. Don't even play that game because you can't. The entire thing is a world of hurt.
Whilst there must be other people doing this, I've only ever met one other person who does what I do (well, one thing that I do). I never do one on one private lessons unless 1) they're willing to pay me as much as a group would anyway (more on that below), 2) they're quite interesting. Even when I have dealt with rich, successful people in the past, a lot of one on ones are like pulling teeth. Many people here literally base their entire lives around working a desk job, eating and shopping (and outsourcing their kids if they have them). Even when they travel abroad, most of them having nothing interesting to tell. Avoid "conversational English" like the plague, though you may want to do one on one test prep (something I've never done). One on one kids are often doing it under duress from their parents. Teaching one on ones is like self-lobotomising.
On the other hand, I would recommend setting up groups. Indeed, you can often find one enthusiastic mother/socialite who will happily do all the leg work for you in this respect. I've done this both with adults and kids. One benefit is that there's a much higher level of energy with the group dynamic. This is good for both the teacher and the students. Another benefit is the money. You could, for example, charge $30-40 for one person, or you could charge $10/person x 8 people. That's the way I first started (i.e. a fixed rate per person and a minimum class size), but now I charge a flat rate to open a class, up to three students. After that, it increases by increments for each additional student. I earn more, they effectively pay less per student the larger the class is. Win/win. It also gives them an incentive to go out and find more students for you. A flat rate is a disincentive because they pay the same to share the class.
As mentioned by others, there are plenty of other side hustles you can do, especially if they're online and you can take advantage of lower living costs.
I would also recommend avoiding other English teachers for the reasons mentioned above. Even aside from the fact that the industry is full of drunks and other assorted misfits, ESL in Asia is where dreams come to die. It's full of people with zero ambition in life. That can provide opportunities though if you're not like that. The trick is not becoming like that without realising it.
I'll just throw in a few expansions on some of the points that have already been made.
Private lessons are pretty common in Taiwan. It's also a far less xenophobic country than Korea based upon all the people I have known who have lived in both.
The trouble with private lessons is that, as with English teaching generally, the market is completely saturated unless you live outside a large metropolitan area or you're willing to do something different. Every single other sociology major from a state university in the US, plus seemingly half of Canada and South Africa, has already thought of coming here to pay off student debt. There's a bit of a race to the bottom with private tutoring in Taiwan or with the industry in general. I have known people here who have saved crazy money in a very short time, but that can be pretty difficult if you need to get your visa through your job. The cram school industry here is notoriously exploitative. It's also full of enablers: fat South African chicks who don't have boyfriends and will never get boyfriends. Bosses here are aware of this, even if only at an instinctual level, and they are also aware that said women cannot/will not leave Taiwan. Therefore, if they want someone to make posters on a Saturday night at home, there will be lots of willing victims. Compared to such people you can only ever look like a bad employee and so will have to endure massive amounts of bullshit as a result. Don't even play that game because you can't. The entire thing is a world of hurt.
Whilst there must be other people doing this, I've only ever met one other person who does what I do (well, one thing that I do). I never do one on one private lessons unless 1) they're willing to pay me as much as a group would anyway (more on that below), 2) they're quite interesting. Even when I have dealt with rich, successful people in the past, a lot of one on ones are like pulling teeth. Many people here literally base their entire lives around working a desk job, eating and shopping (and outsourcing their kids if they have them). Even when they travel abroad, most of them having nothing interesting to tell. Avoid "conversational English" like the plague, though you may want to do one on one test prep (something I've never done). One on one kids are often doing it under duress from their parents. Teaching one on ones is like self-lobotomising.
On the other hand, I would recommend setting up groups. Indeed, you can often find one enthusiastic mother/socialite who will happily do all the leg work for you in this respect. I've done this both with adults and kids. One benefit is that there's a much higher level of energy with the group dynamic. This is good for both the teacher and the students. Another benefit is the money. You could, for example, charge $30-40 for one person, or you could charge $10/person x 8 people. That's the way I first started (i.e. a fixed rate per person and a minimum class size), but now I charge a flat rate to open a class, up to three students. After that, it increases by increments for each additional student. I earn more, they effectively pay less per student the larger the class is. Win/win. It also gives them an incentive to go out and find more students for you. A flat rate is a disincentive because they pay the same to share the class.
As mentioned by others, there are plenty of other side hustles you can do, especially if they're online and you can take advantage of lower living costs.