As an alternative, you can take a look at Tie::File. This would let you handle the file as an array. Here's a completely untested piece of code, just to give you the idea:

tie @l, "Tie::File", $file or die $!;
for my $i (0 .. $#l) {
    if ($l[$i] =~ /Error Occurred/) {
        while($i > 0) {
            $i--;
            if ($l[$i] =~ /(A|B):\d+/) {
                print $l[$i];
                exit; # or last
            } elsif ($l[$i] =~ /^====/) {
                exit; # or last
            }
        }
     }
}
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However, Tie::File is not that efficient on large files.

Another alternative could use a combination of a normal filehandle to go forward in the file, and File::ReadBackwards to go backward in the same file.