Selling car – what about taxes and mandatory insurance?

Planning to sell my kei-car privately. It still has 11 months of shaken and jibaisekihoken on it. Taxes for 2024 have been paid. As far as I've understood the jibaisekihoken is bound to the car not the driver.

So what happens when I sell the car? Do I take extra money from the buyer for the remaining time of the insurance/taxes? Or is there a refund when completing the name change at the light vehicle inspection office?

Any help is much appreciated! Thanks a lot!