That (*SKIP:name) precedes (*MARK:name) in your pattern makes no sense, and leads me to think you believe a MARK is akin to a label and a SKIP is akin to a goto. That is not the case at all.

What we're marking and skipping to are positions in the string being matched.

(*MARK:name) bookmarks the current match position under the provided name.
(*SKIP:name) prevents everything before the named bookmarked position from being part of the final match if we backtracking through this.
(*SKIP) prevents everything before the position from being of the final match if we backtracking through this.
(*SKIP) is basically the same as (*MARK:anon)(*SKIP:anon).

Solution:

if ( "aab" =~ /(.)\1(*SKIP)(*FAIL)|.*/ ) {
   say $&;  # b
}
[download]

(*SKIP) was matched at position 2. When (*FAIL) caused the matching to backtrack through (*SKIP), everything before position 2 was eliminated from potential matches.

Non-trivial example using (*MARK:...):

If instead you want ab, you could use

if ( "aab" =~ /(.)(*MARK:go)\1(*SKIP:go)(*FAIL)|.*/ ) {
   say $&;  # ab
}
[download]

This time, only the text before position 1 was eliminated from potential matches.