I don't think your solution is that bad. If you want to get rid of the two reverse, I think you have to buy and additional list function instead, for instance:

List::MoreUtils::after_incl {
    $_ !~ /DBIC/
} List::MoreUtils::after_incl {
    /DBIC/    
} List::MoreUtils::before { 
    /Dancer/
} @YourList
[download]

I consider this even more ugly. Alternatively you could try

my $partition=0;
my @parts =
List::MoreUtils::part {
    if($pivots[0]) {
        if($partition % 2 == 0) {
            if($_ =~ $pivots[0]) {
                ++$partition;
            } 
        } else { 
            if($_ !~ $pivots[0]) {
                ++$partition;
                shift @pivots;
            }
        }
    }
    $partition
} qw<eval DBIC::3 DBIC::2 DBIC::1 MyApp::3 MyApp::2 MyApp::1 Dancer::3
+ Dancer::2 Dancer::1>;
print join(',',@{ $parts[2] }),"\n";
[download]

Whether this is more readable, is something to be questioned, but at least the code can be generalized easier to more than 2 "pattern changes". However, it silently assumes that part traverses the list left to right, which is not guaranteed by the documentation.

Another solution (which does not use reverse) would be

my @input=qw<eval DBIC::3 DBIC::2 DBIC::1 MyApp::3 MyApp::2 MyApp::1 D
+ancer::3 Dancer::2 Dancer::1>;
my @firsts=@input[0..@input-2];
my @seconds=@input[1..@input-1];
my $inside=0;
my @result;
List::MoreUtils::pairwise { 
    if($inside == 1) {
        my $pat=qr(Dancer);
        push @result,$a;
        if($a !~ $pat && $b =~ $pat) {
            $inside=-1;
        }
    } elsif($inside == 0) {
        my $pat=qr(DBIC);
        if($a =~ $pat && $b !~ $pat) {
            $inside=1;
        }
    }
} @firsts, @seconds;
print("@result\n");
[download]

but this is forcing the pairwise function to something in a way it was not really meant to be used (since the result of pairwise is never used). Maybe you are better off writing a conventional loop and storing the state (inside / outside your pattern sequence) in a status variable, similar to my part example, but without (mis-)using List::MoreUtils.