Using the information in a thread on IH8Mud ( 1985 FJ60 Wagon Horn Problem), I just got the horn working in Dawn’s 60. I used some teeny little rubber grommets, sliced in half, as spacers. Glad that did the trick, since the screws on the cover are stripped.
I’m sure this trick works on FJ40s (at least the late models with the smaller steering wheel, since I’ve got one of those wheels on hand) and FJ62s, too.