You could "sorta" modularize your sendmail.pl. Wrap the main logic of that script into a function (say, sendmail_main()), and add a line like this at the top of that function:

my @ARGV = @_;
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Then, in your calling script, you can:

require 'sendmail.pl';
sendmail_main(@args);
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Inside of Sendmail, you can use caller to discover the name of the calling file.

I highly suggest, however, that you fully modularize your script; you could always use create a new sendmail.pl that did something like:

use Sendmail;
Sendmail::send_mail(@ARGV);
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if you still need to call the script separately.