DNS load-balancing

Hi everyone

I am in an implementation of a network service, but I got the query if it is possible to do some kind of balancing in the Bind Linux DNS server.
Stage
Guest endpoint will communicate via wireless to a captive portal to login, this login page is provided by a server with IP example 1.1.1.1, another redundant server with IP 1.1.1.2 has been placed.
The idea is if server 1.1.1.1 goes down, server 1.1.1.2 will answer the requests.
In my dns server I would have to do
guest IN 1.1.1.1
guest IN 1.1.1.2
From a DNS perspective I see that it will always resolve to these 2 IP's but you won't be able to tell if one of the servers is down.
Once the clients have these 2 IPs in their dns cache, they will continue to use them.
I understand that it would be best to use a specialized hardware balancer for this task.
I would be grateful if someone could give me some suggestion if something could be done at the DNS server level and in any case, in what scenario is DNS load-balancing used?

Thank you very much

I do not recall ever load balancing nameservers. DNS is a thin protocol that does not require heavy bandwidth or processing. There is not that much load to balance unless you are under attack.

I did set up high availability, using two servers and OpenVZ guests. (Today I might use Proxmox or LXC/LXD guests, or even virtual machines.) I set them up master/slave and at different local IP addresses. When they come up, the first one up would take on the nameserver IP address as a secondary, and the other would detect that and idle. If the first one up had issues or went down, the other would send a STONINTH signal and take over the DNS address and start serving.

The setup served us without fail for years, until Corporate decided to outsource nameservices. (New CEO was from India and wanted to outsource everything possible to data centers in India. But that is a tale for another time....)