Maybe you can do better. You've studied a lot more abnormal psychology than I have. Anyway, I'm going to toss you the few known facts about our psycho and ask if you can make any suggestions that I haven't already made. I'll pass them on to the captain. If you can come up with anything at all helpful, it may save a life, or several lives. Here goes:
Both victims were young housewives. Both were attractive. Each was home alone (home was a house in one case, an apartment in the other) at the time of the attack. In one case the husband was out of town on business, in the other working a swing shift at an airplane parts factory.
In neither case was there any sign of forcible entry; the woman herself must have admitted him or at least opened the door for him.
Both women were knocked unconscious with a blow to the chin, then carried to a bed; their clothes were torn off them and they were raped, then strangled to death. Still, from the lack of anything indicating a struggle, unconscious from the knockout. (Don't ask me how the autopsies could prove or even indicate that the rape preceded the strangling but my friend tells me that the medical examiner is absolutely certain, so I'm willing to take his word for it.)
Both crimes occurred in the evening. We happen to know the exact time of one of them, ten o'clock. This was the one who lived in an apartment. The couple who lived in the apartment under hers heard a thud at that hour; they're certain of the time because the husband was just switching channels on the television to get their favorite ten o'clock program. Knowing that their upstairs neighbor was home alone they looked at one another, each wondering whether she might have had a fall and need help. But before either spoke to the other they heard footsteps moving around and decided she was all right, that she'd either dropped something fairly heavy or had a fall that hadn't hurt her.
That was the first of the two murders. We don't know the time of the second one so accurately. The woman's body wasn't found until early the next afternoon when her husband returned from his business trip. After so many hours the M. E. could only say that death had occurred late the previous evening, probably between nine o'clock and midnight.
We know him to be a man of considerable strength, not only from the steam behind the knockout blows he struck but from the way in which he ripped the clothes from his victims after carrying them to a bed. One of the women was wearing a quilted house coat that zipped open about halfway down the front; he tore it the rest of the way, and quilted material does not tear easily.
From the speed and accuracy with which he struck the police theorize that he may be or may have been a boxer. Also, from his strength, they believe he is more likely to be a laborer than a white collar worker. I'll go along with both of these deductions as possibilities or probabilities and not as certainties. A man with no boxing experience but with good coordination and a little luck could have struck those blows. And if he has a good mind (except for its warp) and/or a good education he'd certainly be doing something better than manual labor.
So much for the physical side, and to the mental. First, I do not believe he is a moron. He must have cased those jobs and known that the woman would be alone at the time he came. Otherwise he had incredible luck—and I refuse to credit the incredible. Also, he left no fingerprints at the scene of either crime; he either wore gloves or avoided touching any surface that would take them. A moron wouldn't think of fingerprints.
But to a more important point, the nature of his psychosis. I have a theory; I hope you'll be able to expand on it if you agree or to offer a better one if you disagree.