I love the way you explain things, The Parser!
I think this is one of the first problems that you can encounter when analysing sentences in English.
Fortunately, among the complements, subject complements are the easiest to distinguish.
I used to cut off the sentence to see if it made any sense as The Parser did in his examples. He is tall..He is (¿?)
They usually go with: be, seem, look that are directly related to the subject:
"You look ill"
" My sister is a nurse"