Ah! That's what the OP meant. Unfortunately, there's a bug in your formula.
It displays the first $msg_time messages for $num_msgs seconds.
It should display the $num_msgs messages for $msg_time seconds.
Fixed:
my @message = (
"Message 1",
"Message 2",
"Message 3",
"Message 4",
"Message 5",
"Message 6",
"Message 7",
"Message 8",
"Message 9",
"Message 10",
);
my $msg_time = 5;
print $message[ time / $msg_time % @message ], "\n";
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