using gpg-agent between different sessions

I am trying to set up gpg-agent

When I log in to my machine (via SSH) and invoke gpg, it asks for password every time (it does not start gpg-agent automatically).

When I start gpg-agent manually using:

eval "$(gpg-agent --daemon)"

then next invocation of gpg actually launches the agent, and after typing my password once, I can then use gpg without password. Also, I see a socket has been created in $HOME/.gnupg/S.gpg-agent=

When I log out and log in again (ssh), I see the socket still exists in $HOME/.gnupg/S.gpg-agent= and ps shows that the agent is running, but every invocation of gpg asks for password, as if there was no agent.

I have added this to my .bashrc:

GPG_TTY=$(tty)
export GPG_TTY

but that does not seem to help

I find the behaviour of gpg-agent very confusing. I am familiar with ssh-agent and that behaves straightforward and understandable.

How can I use gpg-agent same way as I would use ssh-agent ?

For comparison, this is how ssh-agent behaves:

After I boot my machine and login for the first time, I launch ssh-add manually and type my pass phrase once.

Then, every time I log in to my machine (X, console, ssh, ...) I can use the agent (I don't need to type my password again). This is done by adding following line to .bashrc:

export SSH_AUTH_SOCK="$(find /tmp/ssh-*/agent.* -uid $(id -u) -type s -print -quit 2>/dev/null)"