Question about postgres replication construction

Hi everyone,

I need some advice.

I need to set up a 3 node postgres 12 cluster.

The primary postgres server with a streaming replication hot standby which
is managed with repmgr.

Besides these 2 servers I need to create another standby server which will
be synced with wal files that are copied to the server.

This third node does not have any connection with the other two nodes and
will only be updated through the wal files.

The third node will be created by taking a base backup of the primary node
and restoring it to the PGDATA directory.

repmgr is not configured for node 3 because it has no connection with the
other two nodes.

The primary connection parameter is uncommented in the postgresql.conf.

This construction works until I perform a switchover from node 1 to node 2
with repmgr, making node 2 the new primary and node 1 the new standby.

The standby on node 3 does not pick up the switch.

My question is: Does anyone have an idea in how to approach this? Is this a
valid construction?

I know I'm missing something essential but at this moment I can't seem to
see it.

Thanks in advance.

Regards

Marian