Here are building a new store, to its's parking site and our one had to cross signal also. It is a "cross two full greens" type lamp, you must give priority to the direct traffic and the parallel way walker traffic if you go to left or only for the parallel walker traffic if you go right, it means the "full green" If in the green signal is an arrow, you have the priority.

I write it, I don't know the American formulas.