How good is your Japanese? Wantedly is commonly used for hiring, you could check on there and ask companies you are interested in. Besides that, I heard from a few people that found part time gigs through tech meetups that happen pretty often.
Since you are only staying 4 months, I think your best bet is through people you know either locally or remotely. Finding a completely new company that is hiring you short term and part time might be a bit hard to find.
