Assuming yours is the same as the one in the pic, the tabs are an inch or so long and are all one piece with the white plastic dingus. They run from the white plastic piece toward the steering column where the nut is. You can see a kind of rough place on the plastic next to that wire where the tab broke off.
If the arm(s) are broken off, they will probably just lie doggo in the bottom of the cowling, not rattle around.
You do need to remove the cowling, and on my '64, that's all you have to remove to get at the switch.
Moss sells both a complete swith ($75) or a repair kit ($25)for the switches on early cars. I assume you will probably have to get the complete switch, as the ones on later cars are not repairable.
Sorry I didn't take a pic of the repaired unit, as looking at another broken one doesn't tell you much about what it should look like.