If the CE comes back on, check for codes.... however, the CE should not come on w/key OFF ...if it does , it is receiving bat votage from somewhere...possible short in harness or possible OVP quirk...
If so, I would check the part# on OVP to see if it has been up-graded [arhieves again]. Only other source I can think of off hand
[ don't have schmatic here ] is fuse for pin 16 at Diagnostic box..
[ but doubt it]
I believe you are getting No code flash at box BC you have cleared the codes and 1 flash does not apper yet [ system has not completed test]

Does the led lamp light when you hold the button down w/key ON ??????
That verifies pin 16 power