IPv6 doesn't work correctly on AWS ELB
Solution 1:
There is a long thread of comments on this question.
The solution is to change the route table to use the IGW (Internet Gateway) instead of the EIGW (Egress-Only Internet Gateway) to route the IPv6 traffic. Routing the IPv6 traffic thru the EIGW, in effect, makes the load balancers private and not publicly accessible.
Solution 2:
I had similar problem but without Egress-Only Internet Gateway.
It was happening because my Application Load Balancer was configured with ELBSecurityPolicy-TLS-1-2-2017-01 and ipv6-test.com only supports up to ELBSecurityPolicy-2016-08.