The -t test checks if STDIN is coming from a tty or not, similar to POSIX::isatty. When you invoke your shell script automatically, redirect STDIN from /dev/null. Like this:

$ cat test.sh
#!/bin/sh
perl -le 'print "Interactive" if -t'
perl -le 'print "Batch" unless -t'

$ sh test.sh
Interactive
$ sh test.sh </dev/null
Batch
[download]