I'm having a similar problem... starts when I release the key. Have checked everything, every wire and plug.
I'm actually toward to damaged ECU. cause I get a back fire when doesn't start and get back the key quickly to OFF. It looks ECU have a short inside or some componment out of range making some on/off job exciting and helping to work
I already reinforced the ECU ground
Just a weird conclussion
Is not definitelly the ballast because brake light at cluster never cames off on the ignition process. It does dim when cranking because is being feeded by ballast working as splice... that's normal. ECU gets the power on same way when cranking at least on earlier models. I have known on laters power comes from starter relay I guess to save the ballast when cranking
Damaged Starter relay ? being a later model is something to check too