What does Jiro brush on his sushi?
He brushes soy sauce on it, because he knows how much is sufficient to season each nigiri. Actually not just any soy sauce, but nikiri:


  A good sushi chef adds all the flavors the sushi needs before he hands it to the customer. He mixes his own sauce and uses it behind the sushi bar. This sauce is called nikiri.


you can see him brushing it here:



According to this other site,


  Nikiri is typically made using a mixture of soy sauce, dashi, mirin and sake. The sauce has a subtle complimentary umami sweetness that is designed to enliven and enhance the flavour of the fish with which it is being served.