again, car registration should be done by the new owner. A bit NOT correct about "by the new owner" part.
Not only by new owner "By 行政書士" also possible but need 委任状 plus.
(If bought at car shop, by car shop staff instead customer usual)
行政書士(ぎょうせいしょし/gyou-sei-sho-shi)??
Certified Administrative Procedures Legal Specialist
(limited laws specialist just not unlimited lows specialist "lawer")
(also 司法書士/しほうしょし/shi-hou-sho-shi possible but not usual)
Their office/事務所(じむしょ/ji-mu-syo) placed
near 陸運局(りくうんきょく/riku-unn-kyoku/registration office) usual.
陸運局 also called 陸運支局(riku-unn-shi-kyoku means brach)
or 陸事(riku-ji) means short of 陸運支局事務所(riku-unn-shi-kyoku ji-mu-syo)
But for 軽自動車(Kei car/Yellow plate small engine one) registation cannot at 陸運支局
also some offices location placed different address but not so far from 陸運支局.
BC K car's office belonging 軽自動車検査協会(Kei-ji-dou-sha ken-sa kyou-kai).
(Light Motor Vehicle Inspection Organization)
陸運支局 is for "White plate" car's mainly office.
(some offices location 軽自動車検査協会 with)
委任状(いにんじょう/i-nin-jou)?
Letter of attorney
http://knowhowrashinban.web.fc2.com/eigode.pdfhttp://car.naru2-shop.com/inin.htmlAnyway, recommend asking at city/town hall
about EN speaker's 行政書士事務所 place or TEL number first.
BC I know all well but would like to explain all process (above last link ステップ/step 1 to 7)
and can not be confirmed your car is llegal one or not. (most important point)
Also "Y number plate" car or not.
If llegal one,paper work need 5 days to a week(next week) fr police station paper work.
http://www2.kek.jp/rso/Living/Buy_Change.htmlCar registraion office work under 2 hr total.(lunch break exist)
Comfirming "Parking place certificate" by Police(not by Police man) need 3 to 5 days(result shows next week).
I didn't check content below(not official documents) all but seems mostly right way.
https://okijets.wordpress.com/lifestyle/cars/(kanji "車庫署名賞" is typo "車庫証明証" is)
Or, someone may knows or gives big hints.
http://gaijinriders.com/ (famous mortorcyclist forum)
https://forum.gaijinpot.com/forum/living-in-japan/travel-transportatio...(one of Old Q)
And some Exporters who also have own YouTube channe seemsl looks like friendly.
http://pacificcoastjdm.com/https://www.micklay.com/http://www.smilejv.com/