Ross, your distributor ought to finction quite happily with an open
circuit (as measured by an ohmmeter), so 20Kohms does not neccessarily
imply it is bad.
When I worked for Lucas (!) they allowed 4 (I think) breaks in the HT
windings of an ignition coil. So there is a good chance that if you
try to measure the resistance of the HT side of the coil it will be
infinite. I could explain why all this works, but not now!
Regards,
Simon
PS. you may have a bad distributor cap -- I'm just pointing out that
the evidence you have presented so far is not sufficient to convict!
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