Japanese license plate
If your vehicle is from a country part of the Convention on Road Traffic (Geneva,1949) you do not need a Japanes license plate or have the vehicle inspection.
Article 4 of the law on the exception to the road transport vehicle law with the execution of the Convention on Road Traffic
http://law.e-gov.go.jp/htmldata/S39/S39HO109.html
says that you are exempt from article 19 of the road transport vehicle law. (that is the part of the law saying you need a license plate issued by the government of Japan).
If you print and carry a copy of that law, maybe you can avoid troubles. (Unless the police actually check to see if your country is part of the treaty.)
However, if your country is not a part of the 1949 Convention, you will be driving illegally.
The penalty of driving a car that has not had the manditory inspection is up to 6 months in jail or up to 300,000 yen (about US$3000) fine.
Note that translations of laws and regulations are my own and are not official. Also, laws and other information may change in the future.
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