Hi 
You seem to be missing a } here:
header /static/* Cache-Control max-age=31536000
}
+ }
photos.natehn.com {
root * /home/nathan/photos/_build
You can validate your config via caddy validate before applying 
Please don’t use caddy start but instead caddy run. Or even better, the systemd service, which you seem to have since you shared some systemctl status caddy.service output.
Please see Problem with with caddy - #2 by francislavoie
That isn’t actually a caddy error but instead systemd trying to tell you, that you are missing the necessary permissions and might need to use sudo (sudo systemctl start caddy.service) or user root.
To actually view the full logs of caddy (when running as systemd service), you would use something like
journalctl --unit caddy.service --no-pager | less +G (and press q if you want to exit again).
Also, with both root * /home/nathan/blog/public and /home/nathan/photos/_build you might be running into file permission issues.
I am more or less in the process of doing a proper write-up about common file permission with caddy (or any webserver really) which would explain that in detail.
But in the meantime, you might want to read:
tldr is basically: Don’t use /home/ but instead /srv/ or /var/www/.
Feel free to ask any additional questions, especially because if anything is unclear or if you encounter any issue 