I believe you can garner a picture of motivation through reading micro-cues, and of course by engaging the student with curious questioning....
Follow-up reading on... micro-expression training? concealed motivation? consider looking at theorists Yalom or even Freud, depending on how deep you want to go.
This is a very good question, indeed. Both students & teachers ought to be highly motivated in order to have an efficient teaching-learning process.
My long career in teaching (at schools & at universities) gave me an experience of detecting the “real” atmosphere in the classroom in 1-3 meetings. I usually start by pinpointing the value of the subject in daily life & in their future work. After that, I begin to raise questions to test their responses & I allow them to ask questions. The rule that is set is: No question is insignificant & we must respect each other.
It is unrealistic to assume that all the class will get engaged instantly. Few of them (~ 5%) will be brave enough to participate but this few will help in lighting many candles & in getting a higher percentage to become involved. Those who are active are rewarded by words of praise & by the 10 % mark that is allocated to activity. In many cases, student become highly motivated by telling the whole class that the persons X, Y, and Z are excellent & are up to the challenge.
Would seeing the light in my students' eyes count? Would smiles count? The students who are motivated stay focused for longer, ask questions to clarify concepts, try and then try a different way!
What motivates me, as a teacher? Certainty, students that want to do well and improve in one way or another draws me to them. Another thing that motivates me a lot is finding a new idea or method to apply that I believe will help my students. When I have no new ideas, my teaching enthusiasm is somewhat reduced. Also, a good collaboration team helps with motivation too in addition to support from the administration.
In my work experiences in special education, the definition of motivation is different based on the learner. For example, for a child with severe Autism they may not be able to make eye contact or communicate their wants and needs. In that instance, we may look at whether they approach us by reaching or moving in our direction. As we shape that behavior, we may see them do that more and more. They may stay with us at a table longer than they had during previous times. We measure those things over time to see an increase in that pattern of "engagement". It's not about getting "compliance"...but about getting the students to WANT to engage with adults in some way by arranging for their motivation and making adjustments.
For learners who are higher functioning, it could be defined as active engagement with the instructor. That is difficult if the teacher does not elicit responses in order to gauge the motivation. It can be a lot of work at first...but once a good relationship or rapport is developed it is easier to measure. So I guess my answer is..."it depends". :)
Sorry for the delay in responding to the other question you posted later.
I think classroom observation is the most common source of evidence to measure teacher’s motivation. A peer observation is the other one. Still, the other one is a self-reported survey of teaching efficacy as it involves several aspects of self-report domains, one of which is instructional efficacy.