At the University of Arizona where I received my Ph.D. just like at your institution all incoming graduate students also had to take a semester long course on pedagogy but it was always taught by a postdoc. The mandatory reading was "How to Teach Mathematics" by Steven G. Krantz but in retrospective, I wish, the mandatory reading had been his other book "A Mathematician's Survival Guide". We did lots of exercises like video recording our lectures or grading the same exam (by the whole class) and then comparing the grades.
Besides already mentioned Arnold's article (some of ideas from that article are also eloquently presented in his Ordinary Differential Book 1st one not the Geometric Methods) I really, really like the following writing
by Anatole Katok which is indeed geared towards more advancing courses which you will probably not have opportunity to teach as a TA.
I do not agree with everything Professor Katok is saying but it is a great reading. For example:"After that the picture gets filled in, sometimes straightforwardly using the most elegant or most useful available arguments". I quite on the contrary believe that the picture should be filled by the arguments which the most instrumental in exposing key ideas. I also do not believe in well polished statements of the results as they are usually result of many iterations of the original idea/discovery. I like to state result in its original form when it was discovered (for example Stokes theorem can be stated on the square in $R^2$ in which case its proof become a trivial exercise in applying Fundamental Theorem of Calculus). My advisor Qiudong Wang is a master in delivering such courses (Dynamical Systems, ODE) which are completely revealing.
As of teaching courses taken by unmotivated learners (intro college courses) I have much less to say and in my experience you have to treat crowd on case by case basis. I am not sure that any reading can help you with that (you have to get experience).