I would put a subroutine into @INC that simply logs all the filenames/module names that get loaded, likely into a text file named after $0 (the currently running program). I'd use a text file to avoid any hassle with the database, just for the case when it is unavailable.

If you can set up $ENV{PERL5OPT} for every user, you can install the hook for every user:

package LogLoadedModules;
use strict;

sub log_loaded_module {
    my( $self, $file_to_load ) = @_;
    write_to_log_file( $0, $file_to_load );
    return; # we didn't find anything
}

# Automatically install the hook in @INC when this
# module is loaded
sub import {
    unshift @INC, \&log_loaded_module;
}

1;
[download]

Then you can set up @INC for every user by having

export PERL5OPT=-MLogLoadedModules
[download]

Update: Fixed unshift line, as corrected by Perlbotics