Recruiting process time for assistant professor position in Japan? What time scale is typical for the evaluation of applications for an assistant professorship in Japan?
It depends on the position, but couple of month is a reasonable scale. If you go through the first round (your resume is picked, which itself easily a month), you are contacted for an interview generally at least a month before the interview. However I have seen cases when it took months just to appoint an interview. 

Note that many assistant professors are getting jobs by internal promotions and not through public advertisement.