The lights are on, but nobody's home, meaning that the person gives the appearance of being alert and attentive but they really are not. Sometime this is because the subject is beyond their comprehension, but it is also used to mean that they are more generally incapable of coherent thought (i.e., they are not very smart). (ref, ref)
Poor Jen tried to keep up with the conversation. After returning from so long in that backwater on the west coast, we could see that all the lights were on, but nobody was home.
This is not a phrase one would use when referring to oneself.
Closer to your own phrase is he's as deaf as a post (ref), with the simile attributed to John Palsgrave's Acolastus:
How deaf an ear I intended to give him ... he were as good to tell his tale to a post.
This is literally about the ability to hear, and not about ability to comprehend, and could be used in a self-deprecating reference. I might say to someone (although many hearing impaired people would refuse to make such an admission):
You know I'm as deaf as a post, and I can't hear anything you're saying with all of this racket.
But shorter is better, and one wouldn't usually be so emphatic about oneself, so
You know I'm deaf...
would be better.
It is similar to the invective he's as dumb as a post, but that would not be used reflexively because it refers to one's intelligence rather than one's ability to speak.