How to handle failover with only two servers?

Hey guys,

I have two servers, my primary server and a failover server. I know, ideally I should have a separate server acting as a failover server but in this case, I only have two servers.

The website is a basic WordPress site running on Ubuntu with Nginx. The primary server is Server A. if Nginx goes down on Server A, I would like for traffic to be redirected to Server B. What's the best way to solve this problem?

Thanks!