The same thing happened to me on a 4.3 Chevy engine. It had something like tiny #8 screws. I took the distributor out and put it in a drill press vise. Important: I filed or ground the broken off screw end flat so I could get a center punch mark right in the middle.
I started out with the smallest drill in my cabinet and drilled using a drill press at a high speed. (It always walks to one side anyway.) I kept upsizing the bits ever so slightly until the hole hit the threads on one side. If I'm lucky, I can then get the rest of the broken screw out with pliers and preserve enough of the female threads to hold the new screw.
On the distributor I did, one of the drilled holes walked a bit too much. I did get the rest of the screw out, but I wound up re-tapping the hole up a size and using a little larger screw to hold the cap down. I think I had to drill out the hole in the cap a little to use a bigger screw, but it looked and worked OK.
I started out with the smallest drill in my cabinet and drilled using a drill press at a high speed. (It always walks to one side anyway.) I kept upsizing the bits ever so slightly until the hole hit the threads on one side. If I'm lucky, I can then get the rest of the broken screw out with pliers and preserve enough of the female threads to hold the new screw.
On the distributor I did, one of the drilled holes walked a bit too much. I did get the rest of the screw out, but I wound up re-tapping the hole up a size and using a little larger screw to hold the cap down. I think I had to drill out the hole in the cap a little to use a bigger screw, but it looked and worked OK.
