Oil burner runs for at least one cycle then safety locks out
I wanted to share the additional steps I took to troubleshoot the issue and describe what was ultimately causing the issue. The problem comes down to a weak and short spark.  I was able to test the spark and witness that it was very quick and dim. I replaced the transformer and the protector relay. I likely did not have to replace the protector relay but figured it could not hurt. A retest with the new components showed a strong spark. Now I am back in business and should not have to worry about either of those components for years to come.