I never taught anyone back home, but I have to imagine the experience is very different from the one I've had in Japan. For one thing, I don't believe there are as many people who pay a decent amount of money to study as adults. Since language lessons are big business, a lot of places will try to entice students into taking lessons by offering a freebie of some sort. When I worked at Nova in what feels like another lifetime, these freebies were called "demo lessons" and were supposed to take about 10 minutes. My husband's school offers them as a means of checking a student's level and they take 20 minutes. The agency that sends me students gives away a full one-hour "trial lesson" on occasion, though I get paid for such lessons so the company absorbs a loss.
Most of the trial students will take the lesson and consider whether they feel comfortable with the teacher's character and teaching style as well as the atmosphere or environment. Once in awhile though, I'll get a student who I can tell never had any intention of continuing with a full course of lessons and I just know won't be back. I imagine these students are scoping out a variety of ads for free lessons and go around using them up one at a time to avoid the relatively high price of lessons.
Of course, I cannot know for sure that these students are doing the language equivalent of eating the free sample with no intention of buying the full-size product, but there are some signs which indicate someone may be such a student. The most objective indication is that, after the trial lesson, the student never communicates with the referral agency again. The agency repeatedly contacts such students and leaves messages, but they never get a "yes" or a "no" about continuing. While I know the Japanese are reluctant to refuse, I also know that it's easy enough to make up a reasonable excuse to say "no" (and to e-mail that answer to avoid an uncomfortable phone call). At the very least, a student can claim their beloved dog died and they're too sad to study now, or they think they'd do better in a group lesson instead of a one-to-one lesson.
Beyond the lack of contact, I can sense something during the lesson which is different. I've had three students who I suspect were freebie hunters and that's been enough to make a pattern clear to me. I should note that the lessons always went well with these students. They were engaged and appeared to enjoy themselves. They took notes, responded assertively to questions and paid attention. The atmosphere around such students is different, however.
There is a razor thin bit of nervousness which I presume comes as a result of feeling they're doing something "wrong" ("stealing" a freebie with no intention of following through). I would consider this nervousness part of speaking English except that the sense is different and I've asked these students (as I ask everyone in the first lesson) if it's their first time in a foreign person's home and if they are nervous. For the record, if a Japanese person is nervous and you ask, they don't lie and say they are not. They always admit it if they are nervous.
The other thing which I notice is a lack of desire to "connect" with me. Students who are in for the duration have an air of eagerness to create a certain relationship with me. The energy of someone reaching out to you is discernible, and when that energy is absent, particularly when you have plenty of experience with it being present, you can detect it.
It's actually rather reassuring being able to "read" the intent of a student who is taking a trial lesson. When you're in a position where you're being evaluated, it's nice to know that sometimes you're not going to keep a student no matter how well things go. It's does a good job of mitigating any feelings of failure at not scoring a new "regular".