multi-hop tunnel in the background; killing local tunnel does not kill remote tunnel

Run both ssh-s locally. First connect to the jump server and create a tunnel that will allow you to ssh to the remote host from the local computer:

ssh -fN $jump_host -l $jump_host_user -L ${helper_port}:${remote_host}:22

Then use this tunnel to connect to the remote host, creating the desired tunnel; still from the local computer:

ssh -fN localhost -p $helper_port -l ${remote_host_user} -L ${port}:localhost:${port}

Since the two ssh processes are local, you can kill them both whenever you like; but I think killing the first one should be enough, try it.

Notes:

• This approach may be inconvenient if your "secondary" ssh relies on specific config stored in ssh_config on the jump host.
• I used lowercase variable names; see this answer.