Two Things Turing Could Do to Find His Own "Proof"
Rather than deliberately flatline, there are two things Turing could easily do - given his near infinite resources - to give himself more of the evidence he seeks.
He could find a top-notch regressionist who would take him back to his past lives and even his life between lives, which for people who have been through it is so convincing he would have no more doubts or fear of dying.
Or he could - again, making use of his ability to access the BEST in every field - find a medium who could contact the other side (not the guy Carolyn has been talking to). Presumably evidence of deceased loved ones knowing things no one else would know could convince him that they survive, therefore that he will survive.
Both of these are non-intrusive, risk almost nothing (except a shakeup of his own preconceptions) and could be done discreetly. So why doesn't he? At worst, he gets nothing - which is where he is now.
Someone willing to flatline for the answers - and he should know that most cases of flatlining produce nothing but unconsciousness; the NDEs are just a fraction of such cases - should be willing to risk expanding his own consciousness.