How do you coordinate the failover? Custom scripts or?

We use custom logic. There are various ways to do it. One way to do it is to poll for the termination signal on the running instance, as part of your app say, and if you see termination coming, trigger a Lambda that supervises the bringup of an on-demand instance. For critical stuff you probably want a backup system that checks instance health and brings up a new instance if the old one is not available ... but you probably want that even if you always run on-demand.