Okay, I will be sure to reach out to my medical school and let them know that modern medicine completely misunderstands the function of cardiac pacemaker cells and the sinoatrial node. They should also check on all the people walking with dysautonomia. I'm sure they will be surprised that their hearts actually haven't been beating this whole time.

The nervous system can control the heart, but the heart isn't dependent on input from the nervous system to beat. Without any input from the nervous system, the heart will continue to beat on its own, it will just lose the vast majority of its ability to adjust based on the body's needs.

The heart is actually not reliant on the brain, as it has its own internal pacemaker. Signals from the nervous system can speed it up or slow it down in response to various factors, but without any signal it will just continue to beat on its own at a very steady rhythm and rate. Around 60 bpm if I remember correctly.

As far as surviving after the drop, I have to wonder what that yank of the rope does to your brainstem. If the pull on the spinal cord causes significant tearing and damage in the brainstem, your entire brain would essentially just "turn off". The brainstem is responsible for regulating your brain activity as a whole. Without the activating signals it sends out, the rest of your brain basically shuts down.

Take my advice and stay out of the lake. It's the slaughterfish. They'll swarm you.