Ignition modules fail when they're hot. Is there anyway you can put it on a hot plate and have it tested? I had one that would cut out on me when I was driving. I could let it cool for 10 minutes and get another 2 minutes of running out of it, 30 total from being dead cold.
The next one I had would run all day, but not start after it was shut off for 20 minutes or so. It had no spark until it sat for 2 hours or more.
They are totally confounding and can be mistaken for almost any problem. But I'm like 4 for 4 in diagnosing a bad one, it is always the first part that I change if I have a start/run mystery.
Bob