Some test code expanding on Jenda's suggestion, partially to satisfy my own curiosity. Interesting problem, hope this is of some help - its rough.
A runtime flag in caller() lets your module evaluate at what stage it is being compiled...

package amIBeingUsed;    # in amIBeingUsed.pm

    if(defined( ${ caller()."::RUNTIME_OK" } ))
    {
        # the flag is set
        print "what took you so long to call me?";
    }
    else
    {
        # still compiling
        print "eurgh, i feel so cheap!";
    }


 
sub import
{
    print " slap!!!\n";
}

1;
[download]

...meanwhile, at the Bat Cave ...

use strict;
my  $module         = "amIBeingUsed";
our $RUNTIME_OK     = 1;

# possible scenarios

use amIBeingUsed;    # "eurgh, i feel so cheap! slap!!!"
eval "use $module";    # "what took you so long to call me? slap!!!"

require amIBeingUsed;    # "what took you so long to call me?"
eval "require $module";    # "what took you so long to call me?"
[download]