* If one is doing it in a cloud and wants to avoid potential issues with the clients behind broken DNS resolvers, then one simply nails the entry point instances to specific IP addresses and in event of an entry point failure, assigns an IP address of a failed instance to a standby instance, resulting in a nearly immediate traffic swap.
* If one is running entry points on physical hardware, then the solution is to bind the entry points to a virtual IP address floating between the instances using VRRP.
* Finally, if one wants to be really super-clever and not drop sessions using controlled fail-over, one does does VRRP + service mac addresses similar to Fastly's faild or Google's MagLev. (But really, this is addressing 99.99999% reliability when in most of business cases 99.9% would do just fine and 99.99% would be amazing ).
Using BGP on a L2 vlan for handling a single digit number of IP addresses allocated to the entry points is akin to using K8S to host a static HTML page.