My next thought is that
drawing data from a cell with a value already in it
the numbers might be text "numbers" which min ignores and would value as 0s.

Try coercing those with leading "--" like this

=AGGREGATE(5,6,--AI5,--N5)

This might confuse AGGREGATE which is expecting a range. The double "--" may cause AGGREGATE to view those as an array which requires a different syntax. I've never tried applying AGGREGATE to 2 non contiguous cells.