One picture will do for this word: a hand at someone's back, giving the first push, and then staying still while everyone else moves. That is what instigation names — not the strike, the inquiry or the quarrel itself, but the push that set it going. The hand usually belongs to someone who takes no further part, which is why the word so often comes up when people are asking who was behind something. It leans towards trouble, though it works perfectly well for neutral beginnings too.
From the word’s history
Wiktionary gives the route only: Middle English instigacioun, from Old French instigacïon and Latin instīgātio. The packet does not gloss the Latin root, so nothing more is claimed here.
Wiktionary 只給了傳遞路線：中古英文 instigacioun，來自古法文 instigacïon 和拉丁文 instīgātio。packet 沒有解釋拉丁字根的原義，所以這裡不多作推測。
Wiktionary, "instigation"
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