How do I find out if I'm running interactively or not?

Good question. Sometimes -t STDIN and -t STDOUT can give clues, sometimes not. 

    if (-t STDIN && -t STDOUT) {
	print "Now what? ";
    }

On POSIX systems, you can test whether your own process group matches the current process group of your controlling terminal as follows: 

    use POSIX qw/getpgrp tcgetpgrp/;
    open(TTY, "/dev/tty") or die $!;
    $tpgrp = tcgetpgrp(TTY);
    $pgrp = getpgrp();
    if ($tpgrp == $pgrp) {
        print "foreground\n";
    } else {
        print "background\n";
    }