Hi Steve,
The fuel pump shown will not fill the glass bowl with fuel. I can't say that your fuel pump isn't the problem, but it might be an electrical issue.
Specialty already suggested what I would look at. A failing/degraded coil will have these exact symptoms. They heat up, then kill your spark. They cool back down and work for a while.
I have found that if the condenser is bad, the Willys will run, but not very well. Mine idled rough and had a large noticeable drop in power.
Is your Willys still 6 volt, or is it converted to 12 volt?
Tim