I am a director of our self-managed housing estate's limited company. However, I specifically declined having signature authority over the company back account as we have a sizable reserve. I have to do a FBAR for our personal accounts and did not want to add another to the list.
As a director, you may not need to have anything to do with the back account w/r/t signature authority. That would solve your reporting obligation to the Treasury Dept. As for the IRS, if you receive no income, you have nothing to report on your 1040.