Wooden?? You have to be kidding, except for the RedBull adverdrome. Other than Izu --- nada! almost all other tracks are open to 'public' via collegiate racing and amateur racing programs. Pro tracks used for multi-purpose are also open on practice days. Just show up with proper track gear and talk to the track super .
Tachikawa is surprsingly 'open' for a pro track. Though they don't advertise the practice days - so you generally need to ask at the track (or amateur team director). Many times there are practice sessions before or after an event, too.
FGF has a pretty good database of tracks in Japan, BTW..