Why is the necklace so important? The detectives didn't even take it into evidence until months later, right? Again, if he took it off her that night/early morning, why wouldn't he get rid of it, hide it, flush it down the toilet? It was in the guest room where his mom was staying, right?
I think the state made a HUGE deal of 2 things - the necklace and the dress. The dress turned out to be nothing. He didn't even wash it that morning (imo based on the opinion of SBI, deodorant stains, oily stain). So what that he forgot what she was wearing that night initially.
The necklace too. Why didn't he pitch it if he had to know it would incriminate him?