I tried it like this---the fat comma worked in this case because I added a left curlie and a right curlie to use constant. Without the curlies, MICRO_SEC becomes a bareword:

#!/usr/bin/perl

use strict;
use warnings;

use constant ({
    START           => 1000,
    NO_OF_CALLS     => 1,
    DEBUG           => 1,
    DET_DEBUG       => 1,
    TOTAL_TIME      => 1,
    DETAILED_TIME   => 1,
    RESPONSE        => 1,
    SLEEP           => undef,
    MICRO_SEC       => 1,
});
    
BEGIN {
    eval {
        require "call_simulator.pm";
        use if MICRO_SEC, 'Time::HiRes' => qw(time);
    }
}
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