Hi Dave,
Keep in mind that, of the (2) fuses in the box, the larger is for dedicated to the Horns ONLY. The horns require quite a jolt of power to vibrate and on renewed horns, the power drawn by the horns could fuse the points together or melt internal or external wiring if shorted. As Bob suggests, sounds like you have a dead short but only if the fuse is blown. Before you do anything, I would check with the restorer before I would try anything on my own and see if he would recheck the faulty unit.
If you find yourself on your own, however, I would suggest you consider following the directions offered by Jim Werner in an article on the Healey6 website:
Horn RepairHorns inoperative? The horn contains a set of points that will corrode together. The
small screw is for adjusting the points in the horn and you will probably find that if you
turn it in a little further than it was originally, apply power straight from a good battery
and bash the horn a couple of times it will start to work. Once you get it working you can
adjust the screw for best beep.
Additionally, since your horns were redone, I expect that your problem is not a corrosion issue but one of needing adjustment. As Jim has indicate, I would try readjusting with the small screw.
Good luck,
Ray(64BJ8P1)