You definitely don't need TEFL to find a teaching job easily in Japan but it would give you more options.
I taught in language schools, a junior high, and did corporate classes as well.
It's also quite easy to get hired from abroad, and getting a job while on working holiday/travel visa is a bit of a grey area, although I know plenty of people who have done it.
If I can suggest, from experience, skipping the initial 'just teaching English' thing and apply for undergraduate/graduate school here and teach on the side. I made more money from scholarships (very easy to get) and teaching than I'm making now as a salary man.