I don’t have any experience with arch linux, so I’m afraid I can’t help a whole lot there. I looked up some info on their startup scripts and it seems you should be able to get something working with this:
[Unit]
Description=Sprinklers Pi
After=network.target
[Service]
ExecStart=/usr/local/sbin/sprinklers_pi -L/var/log/sprinklers_pi
Type=simple
[Install]
WantedBy=multi-user.target