I will use fake names for the sake of anonymity. I have recently completed my PhD and applied to a professor position at University ABC. It has been almost 3 months since my application and I sent out an email to the Chair of the department (who presumably is the person in charge of recruiting academic/faculty members) but did not receive any response. There is another senior faculty member at University ABC, Dr. M, whose research is similar to mine and whose work I have referenced in my thesis. Moreover, Dr. M also attended the same university as my academic supervisor but they have never formally met.
Dr. M may not be involved at all in the recruitment process. However, I would like to ask for Dr. M's help in case he is able to give my application a push.
I am not sure how to write an email to Dr. M to ask for his help in such a scenario since there is no reason for me to believe that he is involved in the recruitment process. Nevertheless, I do want this job and I wan to do everything I can to make sure my application gets properly considered. How can I go about this task?