Trouble using pg_rewind to undo standby promotion

I have a primary -> standby 1 -> standby 2 setup with all servers running
PG 13.8 (this effort is part of getting on to a newer version, but I think
those details aren't relevant to this problem). The first standby uses
streaming replication from the primary and the second standby is using a
WAL archive with a restore_command. To make this standby chain work,
standby 1 is set to archive_mode = always with a command that populates the
WAL archive.

I would like to be able to promote standby 2 (hereon referred to just as
'standby'), perform some writes, then rewind it back to the point before
promotion so it can become a standby again. The documentation for
pg_rewind says that this is supported and it seems like it should be
straightforward, but I'm not having any luck getting this to work so I'm
hoping someone can point out what I'm doing wrong. Here's what I did:

First, observe that WAL is properly being applied from the archive. Note
that we are currently on timeline 1.

2024-11-06 09:51:23.286 EST [5438] LOG: restored log file
"0000000100007711000000F9" from archive
2024-11-06 09:51:23.434 EST [5438] LOG: restored log file
"0000000100007711000000FA" from archive
/data/wal_archive/restore_operational.sh: line 2:
/data/wal_archive/operational/0000000100007711000000FB.gz: No such file or
directory
/data/wal_archive/restore_operational.sh: line 2:
/data/wal_archive/operational/00000002.history.gz: No such file or directory

Next, stop postgres, set wal_log_hints = on as required by pg_rewind, and
restart postgres. I also make a copy of the data directory while the
postgres is not running so I can repeat my test, which works fine on a
small test database but won't be possible for the multi TB database that I
will eventually be doing this on.

Now promote the standby using "select pg_promote()" and see that it
switches to a new timeline. You can also see that the last WAL applied
from the archive is 7718/BF.

2024-11-06 12:10:10.831 EST [4336] LOG: restored log file
"0000000100007718000000BD" from archive
2024-11-06 12:10:10.996 EST [4336] LOG: restored log file
"0000000100007718000000BE" from archive
/data/wal_archive/restore_operational.sh: line 2:
/data/wal_archive/operational/0000000100007718000000BF.gz: No such file or
directory
/data/wal_archive/restore_operational.sh: line 2:
/data/wal_archive/operational/00000002.history.gz: No such file or directory
2024-11-06 12:10:15.384 EST [4336] LOG: restored log file
"0000000100007718000000BF" from archive
/data/wal_archive/restore_operational.sh: line 2:
/data/wal_archive/operational/0000000100007718000000C0.gz: No such file or
directory
2024-11-06 12:10:15.457 EST [4336] LOG: received promote request
2024-11-06 12:10:15.457 EST [4336] LOG: redo done at 7718/BFFFFF30
2024-11-06 12:10:15.457 EST [4336] LOG: last completed transaction was at
log time 2024-11-06 12:10:22.627074-05
2024-11-06 12:10:15.593 EST [4336] LOG: restored log file
"0000000100007718000000BF" from archive
/data/wal_archive/restore_operational.sh: line 2:
/data/wal_archive/operational/00000002.history.gz: No such file or directory
2024-11-06 12:10:15.611 EST [4336] LOG: selected new timeline ID: 2
2024-11-06 12:10:15.640 EST [4336] LOG: archive recovery complete
/data/wal_archive/restore_operational.sh: line 2:
/data/wal_archive/operational/00000001.history.gz: No such file or directory
2024-11-06 12:10:17.028 EST [4329] LOG: database system is ready to accept
connections

Next, insert a record into just to make some changes that I want to
rollback later. (What I will eventually be doing is creating a publication
to ship data to a newer version, but again, that's not what's important
here.)

Finally, shutdown postgres and attempt a rewind. The address used in the
--source-server connection string is the address of the primary.

2024-11-06 12:11:11.139 EST [4329] LOG: received fast shutdown request
2024-11-06 12:11:11.143 EST [4329] LOG: aborting any active transactions
2024-11-06 12:11:11.144 EST [4329] LOG: background worker "logical
replication launcher" (PID 5923) exited with exit code 1
2024-11-06 12:11:40.933 EST [4342] LOG: shutting down
2024-11-06 12:11:41.753 EST [4329] LOG: database system is shut down

/usr/pgsql-13/bin/pg_rewind --target-pgdata=/data/pgsql/operational
--source-server="host=x.x.x.x dbname=postgres user=xxx password=xxx"
--dry-run --progress --restore-target-wal

pg_rewind: connected to server
pg_rewind: servers diverged at WAL location 7718/BFFFFFE8 on timeline 1
/data/wal_archive/restore_operational.sh: line 2:
/data/wal_archive/operational/0000000200007718000000BF.gz: No such file or
directory
pg_rewind: error: could not restore file "0000000200007718000000BF" from
archive
pg_rewind: fatal: could not find previous WAL record at 7718/BFFFFFE8

pg_rewind shows the point of divergence as 7718/BF on timeline 1, but when
it tries to replay WAL using the restore command it is trying to find WAL
from timeline 2 rather than picking back up on timeline 1. I tried
setting recovery_target_timeline on the target database to 'current' and
'1' but that gave the same result. Searching the archives, [1] mentions the
need to force a checkpoint after promotion which I tried even though the
problem description isn't the same. [2] mentions a problem that looks more
like the one I am facing but has no responses. At this point I don't know
what to do next and hope someone can point me in the right direction.

[1]
https://www.postgresql.org/message-id/e7b16ddea93a92575cb6d143b6ef602cab22432e.camel%40cybertec.at
[2]
https://www.postgresql.org/message-id/CALp3DH1fLZmPvkOteAbUo4TOLZP-LstKOs6Gcw3Bm7acmJqk=w@mail.gmail.com

Craig