I agree entirely about making sure the switch is actually the problem before replacing it. There are just too many other things it might be.
One way to check the switch would be to temporarily connect the LH switch wire to the RH turn signals, and see if they work now. If not, the problem is somewhere else. Of course, if they do work now, the problem might still be in the wiring to the switch, but at least you've narrowed down the possibilities.
But IMO it would be foolish to do a restoration without disassembling the control head (which includes disassembling the turn switch) for cleaning and lubrication. Although not mentioned in the manuals, I feel this is a "normal maintenance" item that should be done every 10 years or so anyway.
And while it is certainly possible for the components to be badly worn or broken, generally cleaning and lubrication is all it takes. For me, at least, the periodic maintenance helps ensure that it won't get broken (I have broken one, trying to get the signals to stay on
)
Moses is right, of course, about it being possible to replace the head without removing the wires from the car, but I wouldn't recommend it, especially if you're not certain the switch is the problem. Those wires also get old and break sometimes, plus it is rather difficult and fiddly to connect them to the control head. IMO you should get new wires to go with your new control head (if you do go that way).
Removing the head is not very difficult, but you will need to disconnect the wires under the hood (if they aren't already) so that the harness can move at least partway through the tube. There are also 3 small 'grub' screws spaced around the back of the steering wheel hub that need to be loosened. After that, the head just pulls away from the wheel.
To reinstall the wires through the tube, first push a length of steel "handy wire" (aka baling wire to some of us) through the tube. Shape the end into a hook, and tape the wires to it. Some
wire pulling lubricant will help too. Then you just alternate pulling on the steel wire, and helping the electrical wires into the other end.