Did the locals only provide encouragement or were some also actively involved in helping to overthrow the Visigoths?
Oh, and a follow up: Why were the Visigoths so unpopular then?
Hey! There is always room for further discussion, but you might find my previous answer on the conquest useful.
It's not that the Visigoths were unpopular, though there was likely no love lost between local aristocrats and the palatine magnates who had for decades controlled access to the royal center of Toledo. Local capitulation was likely a response to the rapid collapse of a centralized resistance and a desire to preserve the local status quo (rather than monarchical institutions).
Happy to answer any follow-ups you may have.