I don't think Elon musk has any influence on Trump not to say Putin. If he does, then Trump (or should I say his handler Putin) will not want to increase tariffs on Mexico and China where Musk’s companies are located.
To be honest, he is just one of the oligarchs controlled by and affiliated to Trump/Putin and may have helped launder Trump/Putin's money via bitcoins and funneled campaign funds using his company.