Błędnie: He gesticulated with his head to indicate the answer was wrong.
Poprawnie: He gestured with his head to indicate the answer was wrong.
"Gesticulate" oznacza 'gestykulować' (rękami). "Gesture" to 'gestykulować', 'dawać znaki' (mowa tu również o znakach dawanych np. głową). Słowo "gesture" to także 'gest'.