Here is my solution. This is on Debian 8.
Install Dropbox as per standard instructions. So far, I've only got one user connected, I don't know if this will work with multiple users as dropbox seems to register the machine and not the linux user account. If you know how to get multiple user accounts on one server working let us know.
Then install the python control script instructions but put it in /usr/bin and not your home directory bin.
Create file /lib/systemd/system/dropbox@.service:
Description=Dropbox as a system service user %i
# 'LANG' might be unnecessary, since systemd already sets the
# locale for all services according to "/etc/locale.conf".
# Run `systemctl show-environment` to make sure.
Enable the service for user fred:
$ sudo systemctl enable firstname.lastname@example.org
Then start the service:
$ sudo systemctl start email@example.com