引き際、引き時
Unlike Mr Abe, Mr Koizumi timed his departure well.

見え透いた言い訳をする
make a flimsy excuse for

Two days later he stood down on the flimsiest of excuses: that Ichiro Ozawa, leader of the main opposition Democratic Party of Japan (DPJ), had refused to meet him to discuss a compromise over extending important anti-terrorism legislation.