Saw this too recently. I have thought about what I would do in any case like this, the answer is clear: insist on a polygraph test immediately to show the police I have nothing to hide and they can get right to the case and with my help.
I remember a man who's wife went missing, he asked the police to trace her cellphone signal and they wouldn't do it because of rumors that the couple were having problems - the police assumed she ran away. Meanwhile, the wife had busted through a small guard-rail and went 20 feet deep into the woods upside down and unable to free herself from the car and she was hurt.
12 or so days later, a road crew noticed the guard rail and found the car, she was dead but had lived several days, many of those with a charged phone that could have been tracked. I wonder if he dismissed himself as a suspect immediately, might they have tried tracking the phone, rather than look for reasons where she have have gone???
Gone Girl was nothing like my post above, I figured out pretty early on where it was going, it just got more twisted as the truth came out.