Most people you see on camera will have some level of makeup on, however I hear he likes to do his eyeliner himself. (I can only confirm the part before the coma though)
He wears it sometimes. You can tell the pics when he doesn't. I don't think he did at the RNC. I'm sure some conservatives would have been concerned if he did. Men wearing eyeliner is, apparently, more popular in India than in the US. Maybe his wife like it?