ANSWER: Solomon was the wisest man who ever lived by virtue of a gift from God. He certainly thought there was a right time for 'everything under the sun.' This included when to weep, mourn, and die (Ecclesiastes 3:2 - 8).
Like you, I had to decide whether to shut off life support for someone I love and let them die (if that was God's will). Many years ago, I was married to a woman named Jeannette. We had been married for three years when she was 24 years old. The doctors said that although her medical treatments might keep her alive for two or three more weeks, her remaining time would have no quality. The final decision was to shut off her medical equipment. That was fifty years ago, and the decision has never been regretted even though it was a difficult one to make.
Some people say we are playing God by trying to keep a patient alive through life support means. Others say we are playing God by pulling the plug and letting them die. I do not subscribe to either idea, as God can take a person's life while he or she is on a respirator, or prolong it if taken off. God knows what is best, and does not need any advice from us.
The advantage of life-sustaining equipment is they provide relief from the body’s need keep the vital processes functioning, thus making the healing process easier, in the same way putting a broken arm into a cast does. It is simply temporary support. Considering this, the question becomes one of whether to provide help for the body while it heals, or to remove the support and force the body to work harder during the healing process, should God choose to keep the patient alive.
I recommend seriously considering, as I had to, the kind of life the person in question will have if they stay on medical devices that cause them to die later rather than sooner. My wife's doctors informed me that, for however long she lived, my wife would experience an increasing amount of pain. I talked it over with Jeannette and we decided that, in order to give her relief from further agony, the machines connected to her be shut off. Within a few hours of "pulling the plug," she peacefully breathed her last.
Before making such a serious decision, take the time to have a family conference with the doctor regarding the likelihood of your brother living without the respirator. If possible, discuss the situation with your brother. If he is capable of deciding for himself, you should abide by his choice. Finally, there is an autopsy to consider. Again, if your brother is able to make such a decision, act on his choice. Otherwise, it should be a family decision.
Just before she would die, I mentioned an autopsy to Jeannette. She immediately replied, 'If it will help someone else to live, then I want it.' Discoveries made during autopsies have helped thousands of others since that day. If you know of someone who is on renal dialysis, you might consider giving a prayer of thanks for God's use of Jeannette's life to make part of it possible.
Is taking your brother off life support and letting him possibly die the right thing to do in God's eyes? Since only he knows take the matter to him in prayer. God may even make the choice for you by relieving your brother of the burden of living while he is still on the respirator. Regardless of what happens, do not let it cause a rift between you and the family. These regrettable rifts, over time, will hurt more than the loss.