PG 9.6 managed fail over of master, how do i manage a pg_logical subscriber

Hi,
I have the following configuration.

pg9.6_master --> streaming replica pg9.6_standy
--> pg_logical replication of several schemas to pg9.6_logical

We plan to perform a managed fail over of pg9.6_master to pg9.6_standy.
As part of the fail over, the virtual IP address and hostname of
pg9.6_master will be migrated to pg9.6_standy.
I'm looking for guidance on how to keep the pg_logical replication going
to pg9.6_logical from the newly promoted 'master'.

If I shutdown pg9.6_logical prior to the fail over, and start it back up
after the failover, it should come up 'believing' that pg9.6_standby is
pg9.6_master, will it 'just work'? or is there a process that I need to
follow have pg9.6_logical succesfully replicate from the newly promoted
host?

thanks,
reid