Chosen Solution
I’ve found several results on this page for similar problems but with different iMacs. This one has non-removable RAM though so RAM suggestions don’t help. LED 1 never shuts off until I unplug the system. When I press the power button 2 will light up, then 3 will light, and then both will shut off. They will continue doing this until I unplug power. It sounds to me like the logic board failure.
Logic board was the issue.
