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"I was going with сигналить but my dictionary gave me "signal" for that which I interpreted as in signal left or right."

Left or right lamp int the car is 'поворотник'. One can say 'посигналил...

"Car horn" is "клаксон" or "гудок".
"To honk" is "сигналить" or "гудеть".
Also, children teaching includes "cats say 'мяу' (meow), cows say 'му' (moo), .... cars say 'би би' (bee bee)" (it really...