Use 'goad on' when you want to describe someone pushing another to take action, especially with a sense of urgency. The crowd goaded the hesitant speaker on until he finally began his speech.
Pro Tip 2/3
Slight Aggression
'Goad on' often implies a bit of aggression or annoyance; it's not just gentle encouragement. He felt goaded on by his friends' relentless teasing to take the dare.
Pro Tip 3/3
Emotional Connotation
Using 'goad on' can convey feelings of frustration or resistance from the person being urged. She goaded her brother on to confront the bully, despite his reluctance.