Just to bring another bottle to the party and to take up ww's suggestion on input record separator.

$ perl -Mstrict -Mwarnings -MData::Dumper -e '
open my $inFH, q{<}, \ <<EOD or die $!;
[server1]
/tmp/location1/file.log
/tmp/location2/file.log
[server2]
/usr/loc1/file.log
/usr/loc2/file.log
[server3]
/citrix/dir3/file.log
EOD

my %assoc;
{
    local $/ = q{[};
    scalar <$inFH>;   # Get rid of first '['
    while ( <$inFH> )
    {
        chomp;
        my( $server, $fileStr ) = split m{]\n};
        $assoc{ $server } = [ split m{\n}, $fileStr ];
    }
}

print Data::Dumper->Dumpxs( [ \ %assoc ], [ qw{ *assoc } ] );'
%assoc = (
           'server3' => [
                          '/citrix/dir3/file.log'
                        ],
           'server2' => [
                          '/usr/loc1/file.log',
                          '/usr/loc2/file.log'
                        ],
           'server1' => [
                          '/tmp/location1/file.log',
                          '/tmp/location2/file.log'
                        ]
         );
$
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I hope this is helpful.