Early heat seekers wouldn't reliably lock an aircraft from the front, since the heat signature is really only visible from the rear.
Something like this would almost certainly need to be actively guided, but then the RWR needs to be more expensive and that cuts into yacht money for the Lockheed execs.
Sun Tzu isn't in that story, it is a tale about Zhuge Liang and Sima Yi from the Three Kingdoms period.