Thanks, Corion, I think we're almost there. I've got this pared down as far as I can to make an SSCCE. I can't get perl to think I have a valid selector:

$ ./6.1.pluto.pl 
say (...) interpreted as function at ./6.1.pluto.pl line 47.
2020/04/20 20:10:39 Connected to ws://127.0.0.1:40757/devtools/browser
+/10f7d706-4dbd-4073-a438-916f6602fb4c
found the one and only form
Invalid rule, couldn't parse '//*[@name="date", node => $mech->current
+_form ]' at /usr/local/share/perl/5.26.1/HTML/Selector/XPath.pm line 
+283.
$
[download]

Source, with the critical line tried several different ways:

#! /usr/bin/perl
use warnings;
use strict;
use WWW::Mechanize::Chrome;
use Log::Log4perl qw(:easy);
use Data::Dump;
use 5.016;

Log::Log4perl->easy_init($INFO);

my $site =
'https://www.fourmilab.ch/cgi-bin/Yoursky?z=1&lat=45.5183&ns=North&lon
+=122.676&ew=West';
my $mech = WWW::Mechanize::Chrome->new( headless => 1, );
$mech->get($site);

my $guess = 2458960;    #Earth day 2020 in julian days

$mech->form_number(1);
say "found the one and only form"
  if $mech->success();

# my best guess...aka...trial 1
# $mech->field( date => '2', jd => $guess );
# stderr: 3 elements found for input with name 'date' at ./6.1.pluto.p
+l line 21.

# your first guess...aka trial 2
# my @date_fields =$mech->selector( './/*[@name="date"]', node => $sel
+f->current_form );
# stderr: Global symbol "$self" requires explicit package name 

# 3rd guess
#my @date_fields =$mech->selector( './/*[@name="date"]', node => $mech
+->current_form );

# stderr: Invalid rule, couldn't parse '//*[@name="date"]' at /usr/loc
+al/share/perl/5.26.1/HTML/Selector/XPath.pm line 283.

# 4th guess
# my @date_fields =$mech->selector( './/*[@name="date", node => $self-
+>current_form ]');
# stderr: Invalid rule, couldn't parse '//*[@name="date", node => $sel
+f->current_form ]' 

# 5th guess
my @date_fields =$mech->selector( './/*[@name="date", node => $mech->c
+urrent_form ]');

# Invalid rule, couldn't parse '//*[@name="date", node => $mech->curre
+nt_form ]'

$mech->set_field( $date_fields[1] => $guess );

$mech->click_button( value => "Update" );    # this seems similar to W
+M
say "clickbutton succeeded"
  if $mech->success();
my $string = $mech->uri;
say ("We are at $string")
  if $mech->success();
[download]

That lays it out there as starkly as I can. VielenDank und Gruss aus Amiland.