Point 2 of this bug report seems to indicate that the queried site should be passed in URL-encoded. So maybe try with (roughly, untested) the following transformation:

use URL::Encode;
$site_url = url_encode($site_url);
my $req = $wmt->new_request( ... )

[download]

In reply to Re: Net::Google::WebmasterTools: GWMT error: 404 Not Found by Corion
in thread Net::Google::WebmasterTools: GWMT error: 404 Not Found by Frosch

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