Eyer

1654, Edmund Gayton, Pleasant Notes upon Don Quixot, London, Notes vpon Book II. Chap. IV, p. 47, The Amoretto was wont to take his stand at one place about the pew, where sate his Mistresse, who was a very attentive hearer of the man above her, and the sutor was as diligent an eyer of her, for having a book, and black-lead pen alwaies in his hand, (as if he took notes of the sermon) at last he got her exact picture.

You knew less about sex than you knew about sleuthing, but you soon figured out what the goods were and got them. You were not so much a private eye as an eyer of privates.