My gut reaction to the grammatical question you presented is this:
keep it on. 'keep on' is a separable optional phrasal verb, in my opinion. It means something like 'keep the action going'.
Keep the going on.
Keep on going.
Keep it on.
What is on? I think it functions similarly to 'on' in 'turn it on', in 'turn the lights on'. An adverb; on-off.
The bus kept on something. What was it that it kept on? It was going that it kept on. It kept on going. Gerund.
3. Yeah, it works similarly to an aspect auxiliary, but it is not.
Student or Learner