Your point of divergence is in the middle of the 7718/000000BF file. So, you should have 2 such files eventually, one on timeline 1 and the other on timeline 2.
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.
Also, do your archive/restore scripts work properly for history files?
The scripts don't do anything special with history files. They are based on the continuous archive docs [1] and this [2] article the with slight modification to include a throttled scp since the log shipping server is located in a different data center from the promoted standby and there is limited bandwidth between the two. (Also note that the archive script from [2] is adapted to properly handle file transfer failures - the one in the article will use the exit code of the rm command so postgres won't be informed the file transfer fails resulting in missing WAL in the archive.)