Position only by title, resume tips?

What do I put on resume if I am the director of a company by title (through investment), but I have zero involvement and don't work at all in that company?

I want to list it down as my experience because I have a big career gap to fill but I also don't want to be misleading in case there's background check.

I've got a few options:

Director (title)? Business advisory? Business consultant?

Any other suggestions, or just leave?

Ps: I wanna tone it down

Thanks.