as what i've read on another thread :
Review of eligibility : We are reviewing whether you meet the eligibility requirements.
Background check : We are processing your background check. We will send you a message if we need more information.
Means the real thing is started there, so when you have those 2 messages seems good sign, that doesn't say how much time its gonna take but that shows they are working on it...
I am not sure if that actually means the real thing has started.. that's how MYCIC was for me from the very beginning. For some ppl it does means something but for others they have had that from the very beginning