ah, different url/location ...

you don't need a "submit" button to submit a form

you don't need a "form" object to make a HTTP request (ie submit a form)

https://metacpan.org/pod/WWW::Mechanize#mech-post, $ua->post( $url, $field_name => $value,... Content => $content ) -> POST $url, Header => Value,..., Content => $content, WWW::Mechanize::FAQ, lwpcook, Re^2: POST'ing a large File with LWP::UserAgent

$mech->post(
    $hypermutUrl,
    'FORMAT'    => 'FASTA',
    'ALIGNMENT' => '',

##     'upfile1' => '', (file)
##   [ $file, $filename, Header => Value... ],
##   [ undef, $filename, Header => Value,..., Content => $content ],
##   [ $filepath, $filenameInHttpHeaderUnrelatedToFilepath, ... ],
    [ $seqfile , "mahSeqFile$$.fasta" ],
    'INN'               => '',
    'OUT'               => '',
    'MUTUPSTREAM'       => '',
    'MUTFROM'           => 'G',
    'MUTTO'             => 'A',
    'MUTTO'             => 'A',
    'MUTDOWNSTREAM'     => 'RD',
    'ENFORCE'           => 'DESCENDANT',
    'CONTROLUPSTREAM'   => '',
    'CONTROLFROM'       => 'G',
    'CONTROLTO'         => 'A',
    'CONTROLDOWNSTREAM' => 'YN|RC',
    'Analysis'          => 'All',
    'submit'            => 'Run',

  )
[download]

This excellent suggestion is a good start, but it doesn't get me there. I've altered the code to fit my current understanding, but my $mech object, even after the post, still represents the initial page, not the results page.

I'm encouraged that I can in fact retrieve the initial page, but discouraged not to be able to get to the results (whether I upload the sequences as a file via the 'upfile1' attribute, or, as below, include them as a text field). Here's what I have:

#!/usr/bin/perl
use warnings;
use strict;
use WWW::Mechanize;

my $hypermutUrl =
  "http://www.hiv.lanl.gov/content/sequence/HYPERMUT/hypermut.html";
my $mech = WWW::Mechanize->new( autocheck => 1 );

my $alignment_as_string = <<'END_SEQS';
>HIV1-test.CONS
ATGGGATGTCTTGGGAATCAGCTGCTTATCGCGCTCTTGCTAGTAAGTGCTTTAGAGATTTATTGTGTTC
>HIV1-test.1
ATGGAATGTCTTGGAAATCAGCTGCTTATCGCGCTCTTGCTAGTAAGTGCTTTAAAGATTTATTGTGTTC
>HIV1-test.2
ATGGAATGTCTTGGGAATCAGCTGCTTATCGCGCTCTTGCTAGTAAGTGCTTTAAAGATTTATTGTGTTC
END_SEQS

$mech->post(
    $hypermutUrl,
    'FORMAT'            => 'FASTA',
    'ALIGNMENT'         => $alignment_as_string,
    'upfile1'           => '',
    'INN'               => '',
    'OUT'               => '',
    'MUTUPSTREAM'       => '',
    'MUTFROM'           => 'G',
    'MUTTO'             => 'A',
    'MUTDOWNSTREAM'     => 'RD',
    'ENFORCE'           => 'DESCENDANT',
    'CONTROLUPSTREAM'   => '',
    'CONTROLFROM'       => 'G',
    'CONTROLTO'         => 'A',
    'CONTROLDOWNSTREAM' => 'YN|RC',
    'Analysis'          => 'All',
    'submit'            => 'Run',
);

my $page = $mech->content;
open my $FH, ">/tmp/hypermut.html";
print {$FH} $page; close $FH;
warn "saved webpage data to /tmp/hypermut.html\n";
[download]

I would expect the post operation to add the page resulting from that post to my $mech object -- where am I going wrong?

... encouraged ... discouraged ...

Remember www::mechanize: second "submit" invisible to find_all_submits? What is action? You're knocking a the wrong door, the door you want is ...hypermut.cgi

Additional html related wisdom at markup validation