I'm trying to learn how to use ssh-agent. I followed the instructions
at https://www.ssh.com/academy/ssh/agent.

I have a remote machine that I login to over ssh from my desktop and
want to run ssh-agent on this remote machine for further connections to
other machines in a remote network.

If I login once to the remote machine and run "eval $(ssh-agent)" then I
can see SSH_AGENT_PID in the environment. If I login again from my
desktop to the remote machine with a second ssh session, I can't see
SSH_AGENT_PID in the environment. If I run "eval ${ssh-agent}" again,
it starts up a second ssh-agent process.

Is it possible to have only one ssh-agent process running for my user
account and access it from multiple logins?