The Japanese government should not have insisted on administering the third vaccine 8 months after the second one. They should have began it much earlier.
ご質問ありがとうございます。
"The Japanese government should not have insisted on administering the third vaccine 8 months after the second one."＝「日本の政府は3回目のワクチンを2回目の8か月後にすることにこだわるべきではなかった。」
"They should have began it much earlier."＝「政府はもっと早くそれを始めるべきであった。」
ご参考に。
アメリカ合衆国 
