This work for me:

#!/usr/bin/perl

use strict;
use warnings;
use WWW::Mechanize;

my $mech = WWW::Mechanize->new();

$mech->get("https://utdirect.utexas.edu/registrar/nrclav/results.WBX")
+;

$mech->field( "PASSWORDS", "pass", 2 );

$mech->submit_form(
    
    form_name => "logonform",
    fields => {
        
        LOGON => "rc32536",
    },
);

$mech->get("https://utdirect.utexas.edu/registrar/nrclav/results.WBX")
+;
[download]

Second get needed because of JavaScript redirect to this URL on the response page.