... I don't understand ... this line ...

(?(?{ $run[-1] - $run[-2] != 1 }) (*F))

Is that double-eval'ed or executed? What is the '*F' referencing ...

The embedded code is executed.

      +----------------------+------ embedded Perl code
      |                      |
      v                      v
(?(?{ $run[-1] - $run[-2] != 1 }) (*F))
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This is the "(?(*condition*)*yes-pattern*)" regex expression added with Perl version 5.10 (see Extended Patterns in perlre). In this case, the *condition* is the true/false result of evaluating the code. If true, the (*F) (a.k.a. (*FAIL)) backtracking control verb is executed and the match fails and backtracks to the most recent successfully matched substring: a sequence with incrementing values for $3.

... what is the '$^N' ...

The $^N Perl special variable (see Variables related to regular expressions in perlvar) returns the value of the most recently closed capture group.