Looking at similar traouble with OpenVPN, i've found:
https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=876979
and a similar solution seems to work also for arpwatch, eg it is needed
to create the file:
/etc/systemd/system/arpwatch.service.d/after-network-online.conf
With the content:
[Unit]
After=network-online.target
Wants=network-online.target
