If you absolutely need __DATA__ in a BEGIN block, you have to roll your own __DATA__ handling (opening and positioning, i.e. skipping all until the __DATA__ token):

package Foo::Bar::Quux;

print "now in runtime...\n";

BEGIN { 
    (my $package = __PACKAGE__) =~ s!::!/!g;
    my $file     = $INC{$package.'.pm'};
    open DATA , '<', $file
        or die "Can't open '$file': $!\n";

    my $data = 0;
    while (<DATA>) { 
        /^__DATA__$/ and $data = 1 and next;
        next unless $data;
        print "DATA: $_";
    };
}
1;
__DATA__
foo
bar
quux
now in runtime...
now in main
[download]

qwurx [shmem] ~ > perl -e 'print "now in main\n"; use Foo::Bar::Quux'
DATA: foo
DATA: bar
DATA: quux
now in runtime...
[download]

That's for a module. In a script, you would open $0.

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}