What you're trying to do is use 'symbolic' (or 'soft') references, which is officially Frowned Upon (and for good reason), not to mention precluded by the  use strict 'refs'; stricture (one of the strictures that  use strict; turns on). See discussion at Symbolic references in perlref, search PM for more comments. This stricture is turned off by the  no strict 'refs'; pragma. See strict.

What you may want to do is something like this (I'm using your original module):

use warnings;
use strict;

use Test::More 'no_plan';

BEGIN { use_ok('Mysimple_mod', qw (external) ) };

my $mod = 'Mysimple_mod';

ok ( defined( &external ),               "#2 external is defined");
ok ( defined( &Mysimple_mod::internal ), "#3 internal is defined");
ok ( defined( &Mysimple_mod::bogus ),    "#4 bogus subroutine");
ok ( defined( &{"${mod}::bogus"} ),      "#5 bogus subroutine");

my @softies = qw(internal);
# my @softies = qw(internal bogus);

for my $softy (@softies) {
    my $func = "${mod}::$softy";
    no strict 'refs';
    ok( $func->(3) ==  9,  qq{invoke soft ref'd func $func( 9)} );
    ok( $func->(3) == 10,  qq{invoke soft ref'd func $func(10)} );
    }
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Output:

C:\@Work\Perl\monks\gctaylor1>perl test_soft_refs_1.pl
ok 1 - use Mysimple_mod;
ok 2 - \#2 external is defined
ok 3 - \#3 internal is defined
not ok 4 - \#4 bogus subroutine
#     Failed test (test_soft_refs_1.pl at line 77)
not ok 5 - \#5 bogus subroutine
#     Failed test (test_soft_refs_1.pl at line 78)
ok 6 - invoke soft ref'd func Mysimple_mod::internal( 9)
not ok 7 - invoke soft ref'd func Mysimple_mod::internal(10)
#     Failed test (test_soft_refs_1.pl at line 87)
1..7
# Looks like you failed 3 tests of 7.
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See what happens if you add  bogus to the  @softies array.