Actually sounds kinda’ phoney to me that he’d basically confess to both murders...
I doubt he 'confessed', I suspect they have the evidence he did it, video, DNA and his body is probably marred with the struggle... Then of course there is that laptop which no doubt the authorities have. He probably was offered better conditions and a shorter prison time IF he admitted what the evidence demonstrates...
He most likely figured out he would never leave Peru alive, and his days of terrorizing women are at an end.