I think you are configuring something wrong here. I can confirm the SSH access even when the elastic IP is attached to the non-primary (eth1) n/w interface.
To elaborate my setup, I have setup following things:
- An EC2 instance inside the public subnet of a VPC.
- Two network interfaces without any public IP address auto-assignment.
- Security group which allows SSH access from my local machine.
- Elastic IP attached to eth1 (non-primary) interface.
Following command is used to connect to the instance.
ssh -i /path/to/identity/file -vvvv ec2-user@<public-dns-of-elastic-ip>
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