"Not to scare you, I just want to prepare you that the process truly seems random and arbitrary in many respects."
I agree. And, that's true of any job in this field including clinical ones. There's no magic bullet, dot the Is, cross the Ts approach that will work every where, every time. I am sure if I applied for internship again the next year, I might have had different results. On job interviews, academic ones where you give a talk or two (as I've had to do), do followup interviews (2 and sometimes three followups, multiple phone followups), all it takes is one person not to like something and if they express it in a way that is compelling to others, you are done. Or, if it is the wrong person, it doesn't even have to be compelling, you are just done. Your fate might even be sealed before you even applied and set foot at the site for interview. Let's say there's one neuropsych spot at a site you want to go to and a faculty member that is very well connected to the site in some way or famous or whatever, has a student that wants that spot, calls are made, then your interview is effectively a formality. There's nothing you can do short of walking in there with publications in Nature, independent funding and a mentor that trumps the other one in notoriety and, even then, it might not work. I've interviewed at one place for postdoc where the following was said to me, "You are a superstar. I'd offer you the position right now, but I'd like you to think about it for a week and talk to me" and at another two sites I was verbally offered the positions complete with at one "You are great. I can only pay you xxx (NIH postdoc levels). It should be illegal, but welcome aboard" only to have none of three sites extend a viable offer. Faculties can be large. And, priorities of one group may be different than another. Someone may think you are a nice research fit and someone that could develop an independent line of research and another faction may want a clinical workhorse and not want to deal with a postdoc who is trying to submit grants. In jobs, someone might want a child person whereas another wants an adult focused person. Someone may see you as competition or that your allegiances align too much with another group and would affect the political dynamic in a fashion adverse to them. Also, jobs may be advertised that aren't truly open (created with a specific candidate in mind). Thus, I'd be aiming for position types/responsibilities over specific locations. Flexibility is important in my opinion.