The 10k resistor attenuates tach signal, such that secondary spark triggers are reduced or eliminated. A spark event has initial high voltage peak, followed by decaying oscillating peaks. A tach should just read first peak. Additional peaks add to indicated RPM.
Viewing coil primary with scope and appropriate voltage rated probe may reveal other issues such as plug cables. Each cylinder fire should have similar signal.
Man Dave, good to see you!!! Another thing I was thinking is that IF he does not have a good radio suppression cap on the coil + that might be an idea. It will help keep the coil power from spiking due to coil feedback.