Somehow I missed all this. This is a GREAT example of WHY GOOD TROUBLESHOOTING (and in this case add the word "simple") can save a lot of time and grief
LET'S GO OVER THIS.
For the naysayers, I KNOW that electron flow is neg to pos. But I tend to thing the other way in automotive. What do we have?
We can forget the key/ harness because the OP has said that he has 12V to the coil
So we have a coil, the distributor lead eyelet terminal on the coil Neg, the distributor primary lead, the eyelet on that wire to the points, the actual points, the connection to the advance plate, allegedly in contact with the distributor case, and allegedly the distributor grounded to the block
So here we sit. 12V on coil +, on coil-, I assume 12V at the points terminal. All you need to do is run through the circuit.
Probe coil +, 12V. Probe coil -, 12V. Probe the points terminal, I assume 12V. Probe the points mounting frame, do we have 12? Probe the advance plate, do we have 12? Probe the CASE, do we have 12?????
The point (ha ha, pun intended) is that with about 1 minute at the outside and any cheap meter or in this case even a test light, you can run this down
HOW DID YOU KNOW the points were conducting. You said "they were closed." That does not mean they were making contact. So if you had 12v at the points wire terminal BUT NOT 12V at the points mounting frame, then you would have KNOWN that the points are actually oxidized or maybe not for certain closed. Or if you had 12V on the advance plate but not on the dist. case, then you would have known that somehow, even tho improbable, the advance plate was NOT grounding to the case.
Factory dual point distributors had ball bearing advance plates, and had to have a separate grounding wire to get a good connection between the plate and the distributor case. That does not mean that single points dist's can't have the same problem.