A theory on why the mad man couldn't be ryang eom.
There are 23 years age gap from the present time line, Spring of 1659 (the 10th year of hyojong's reign) to the flashback Spring of 1636 (the 14th year of injo's reign).
We don't exactly know their age. But let's assume that ryang eom was a man in mid 20s to late 20s when we first saw him. And if he's the one inside the cell, he should be around 40 something years old.
But I noticed that all the hair of the man behind the cell already turned grey. He shouldn't be that old at that moment if he's ryang eom. It could only be ryang eom if he has a special gene that makes his hair turn grey at the younger age.
For comparison, gilchae's father hair wasn't even that grey at the current time line (ep 6). I'm not sure but apparently he's around 50?
researchers said that asian people tend to have grey hair later. and the chance to get full grey hair at the age of 50 is a fifty-fifty. among the population, only 1% has full grey hair at 50. of course, that is actually a huge number.
in conclusion it can only be ryang eom if he has a special gene or if he's one of 1% of the population.
and when rewatch 1st episode, the inspector asked him "are you the loyal subject of the late crown prince?" ryang eom was never been his subject, let alone loyal to the cp as he always been looking up to lee jang hyun. if he was cp's subject because he affiliated with lee jang hyun, that's a bit understandable. but to say that ryang eom is cp's loyal subject is a bit too much and doesn't really describe him.
the only cp's loyal subject I can think of is the eunuch. he's around 40s currently, and he'd be in his 60s two decades later. the chance of him having a total grey hair is bigger than ryang eom.
and the eunuch matches with the profile of the man standing behind the hospital cells. I had a doubt at first because the man seems to have a certain admiration and longing when the inspector mentioned lee janghyun. but thinking back, ryang eom and gilchae are not the only persons who like lee janghyun. from the start, the eunuch already acknowledged his skill and he relied a lot to him. if he's the eunuch, the emotional feeling when he heard jang hyun's name is make sense too.