A different kind of cold e-mail

Yes, I realize there are many posts about cold emailing and I think I have the basics down, but this situation seems a little tricky...

In Japan teaching (so completely unrelated to career goals), I applied a couple of weeks ago for a position with a major American company here and got an email back rejecting me (it isn't something that they hire annually, more what seems to be a special, one-time hiring issue). Since then, I have seen they posted the position again (making me think they didn't get any good candidates the first time around). I also found the contact information for someone listed in my alumni database (although, he's actually a parent) who is a partner at the firm. Since this is kind of an immediate situation, I'm not sure what I should say in order to get through to him that I'm hoping to get the job. With other alumni in the country, I've just been asking for tips/advice/insight into how to get started here in Japan, but this is for a specific job with a job (re)posting that is about two weeks old, so I feel like time is of the essence. Should I just say "I saw FIRM NAME had a posting for JOB TITLE, I'm wondering how to best position myself for an interview" or should I say something more along the lines of do you have any advice in general and then if he responds, turn the conversation towards that specific job...