Are you archiving WAL on the promoted machine in a way that your restore_command can find it? Check archive_command and archive_mode on the promoted machine.
No, the promoted machine is not archiving. How should that work? Is it OK for a log shipping standby that uses restore_command to also push to the same directory with an archive_command or would that cause issues of trying to read and write the same file simultaneously during WAL replay? Or should I be setting up an archive_command that pushes to a separate directory and have a restore_command that knows to check both locations?
Hmm, as I write that out, I realize that I could use archive_mode = on instead of archive_mode = always to avoid the potential for read/write conflicts during WAL replay. I can try this later and report back.
Setting archive_mode = on and a restore_command that reads from the WAL archive did the trick. With those changes in place, I was able to successfully run pg_rewind and get the promoted standby back onto timeline 1. Thanks for the tips.