Let me throw in some assumptions here (having to deal with quite a few other text-based formats at work):

• You can skip the headers, because they are standardized across files
• Everything before the first number (or minus sign) is the location name
• Data columns always contain a value
• The only column that can contain spaces is the location name

That means, we can just collapse spaces. We have to handle the location name special, but after that can use split to recover the columns:

#!/usr/bin/env perl

use strict;
use warnings;
use Data::Dumper;
use Carp;

my @sites;
open(my $ifh, '<', 'eclipse.txt') or croak($!);

# Skip header
for(1..5) {
    my $tmp = <$ifh>;
}   

while((my $line = <$ifh>)) {
    chomp $line;
    next if($line eq ''); # Ignore empty lines

    my %entry;

    $line =~ s/\ +/ /g; # Collapse spaces

    if($line =~ /^(.*?)\s[-\d]/) {
        $entry{location} = $1;

        # Remove location name
        $line =~ s/^.*?\s([-\d])/$1/;

        # Split along spaces
        my @parts = split/\ /, $line;

        foreach my $name (qw[long1 long2 lat1 lat2 elevation h m s PA 
+Alt]) {
            $entry{$name} = shift @parts;
        }

        push @sites, \%entry;
    }
}   

close $ifh;

print Dumper(\@sites);
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That results in an array of hashes:

$VAR1 = [
          {
            's' => '59',
            'elevation' => '0',
            'long2' => '45.',
            'lat2' => '55.',
            'lat1' => '-36',
            'location' => 'Auckland',
            'm' => '33',
            'h' => '4',
            'long1' => '174',
            'PA' => '313',
            'Alt' => '13'
          },
          {
            'h' => '4',
            'm' => '40',
            'PA' => '326',
            'Alt' => '11',
            'long1' => '173',
            'lat2' => '35.',
            'long2' => '55.',
            's' => '34',
            'elevation' => '30',
            'location' => 'Blenheim',
            'lat1' => '-41'
          },
          {
            'h' => '4',
            'm' => '42',
            'PA' => '327',
            'Alt' => '9',
            'long1' => '175',
            'lat2' => '35.',
            'long2' => '25.',
            's' => '28',
            'elevation' => '0',
            'location' => 'Cape Palliser',
            'lat1' => '-41'
          },
...
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