That's because they're the classic places for 'something' to appear. Like the grand piano that plays by itself, the human anatomical model that moves by itself ...
動き出すとき、ベルが「ちんちん」と鳴る。だから、ちんちん電車。
When it sets off the bell rings, "ding-ding". Thus 'ding-ding-train'.
青信号が出たとたんに動き出す。
Start off on the green light.
まもなく彼は病気が治って動き出すだろう。
It won't be long before he is up and about.
つり革につかまりなさい。電車がすぐ動き出すだろうから。
Hold on to the strap. The train will start to move soon.