The smaller dark green wire does nothing. It may have been intended for an accessory that was deleted from production. There is, however, a thicker dark green ground wire above the horn wires, and it attaches to the frame near the coils. That thick green ground wire is critically important, but the small dark green wire is unused.
The flasher relay has either two or three connecting wires: gray, black and (if it's a 3-pin flasher) a green ground. It's up near the diode in the upper right part of the electrical box.