Besides the question of whether this solves the ability to sendmail on localhost, this code has serious duplication. I would read all four variables from @_, and then determine what to do based on whether the fourth variable has a value or not. Using prototypes for subroutines is deprecated, I would avoid it.

use MIME:Lite;

sub _mailme {
    my ($to, $subject, $runlog, $mksysblog) = @_;

    $msg  = MIME::Lite->new(
          From     => 'MAILER-DAEMON root',
          To       => "$to",
          Subject  => "$subject",
          Type     => 'multipart/related'
       );

    $msg->attach(
          Type     =>'TEXT/html',
          Data     =>"See attachment!"
       );

    $msg->attach(
          Type        => 'TEXT',
          Disposition => 'attachment',
          Path        => "$runlog",
          Filename    => "$runlog"
       );

    if ( $mksysblog ) {
       $msg->attach(
          Type        => 'TEXT',
          Disposition => 'attachment',
          Path        => "$mksysblog",
          Filename    => "$mksysblog"
       );
    }

    $msg->send;
}
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