If you place the seek, with to-end, above the while loop, it'll skip over the existing content the first time you read the file:

use strict;
use warnings;

my $logfile = "/var/log/httpd/agent1_access.log";

open(FH,'<',$logfile) || handle_error();  # typical open call
for (;;) {
    seek FH, 0, 2;      # this clears the eof flag on FH
    # eof reached on FH, but wait a second and maybe there will be mor
+e output
    sleep 1;
    while (<FH>) {
      print "$_";
    }
}
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