I see this hypothetical sometimes asked in a way that holds no appeal: sure, you live pretty well for a few centuries most likely, but at some point of statistical inevitability, you'd end up in a fate as bad as spending billions of torturous years drowning under the ocean, conscious of every minute as your ocean plate is slowly subducted hundreds of miles underground. Is this hypothetical just supposed to be for people who want to feel clever by pointing that out, or is it meant to mark out the people with asymptotically severe time preference?
Let's say you still have to live forever, but you can do or have done to you things that can plausibly end your consciousness. It's not a switch you can will to happen by thinking about it, you have no guarantee you can perform the procedure before your yacht capsizes or your jealous heir buries you alive to claim your inheritance. I'm talking it has to be a mundane method that causes brain death. You check out, while your entropy reversing body continues as a non conscious living organism like a sponge or coral, until the heat death of the universe and beyond. does that image alone cause enough existential dread to reject the deal?
But you can't know the efficacy. Are there drugs that cause brain death? you should study them carefully to make sure they don't just leave you catatonic and unable to advocate for yourself. might your undying body, over billions of years, possibly heal itself enough to restore consciousness, even just slightly? or even a highly advanced civilization could decide to revive you. It might not even be your ego that's revived, but does that matter?
you can't count on physical damage either. A shotgun lobotomy could still just fracture your consciousness into a hundreds of incoherent fragments looping in confused terror on immortal chunks of grey matter.
If you're diligent enough, yeah, you could probably come up with a procedure that has a great degree of confidence in terminating all thought, but there is always a risk of it not executing properly or the people you entrust on performing it not following through. Try and enjoy your money and youth when every day you decide to not take the procedure is a day when something catastrophic could happen to you that would prevent you from ever doing it.
still. It's failsafe to some extent. say something sneaks up on you and you're not able to end your consciousness on your own terms: Your Boeing disintegrates over the ocean on your way back from the Maldives. one expects that over some time period less than eternity, an extreme amount of trauma, boredom, or sensory deprivation would cause insanity that has to eventually resolve into the brain just shutting down, like a computer locking up. though if you're still alive, it's conceivable that your body would try to heal and reboot, and you might intermittently come back to consciousness for a few hours every hundred years.
also, here is a fun CYOA if you like thinking about stuff like this.