It would probably refer to previous context.

I'm thinking of Jack Nickelson and Tom Cruise in that famous scene in (I think) A Few Good Men.  (approximately)    J: What do you want from me?  T:  I want the truth!  J: You can't handle the truth!

"Even I don't know the truth," makes sense as it stands.   "Did you kill her?"  (reply)  "Even I don't know the truth!"  You'd be expected to be the one who really knows the truth.  But maybe you were drunk and don't remember.  Maybe you hit her and she fell and you left. Here, even refers to yourself.  In addition to all the people who don't know the truth about this (and might not be expected to), you too don't know the truth.

"I even don't know the truth," is awkward, and definitely doesn't mean, "even I don't know the truth."  It sort of means, "There are many things which I don't know, and among them  -  in fact, at the top of the list  -  is the truth."   Actually, your #2 would always work better in this particular situation.

(I thought I had a situation where it might work, but for the moment I'm giving up on it.  Sorry)

Best wishes,  - A.