How to tell systemd-logind that the session is not idle, without using a desktop environment or session manager

I want to use logind for power management. After 30 minutes of inactivity, I would like the computer to suspend.

Problem is, right now, it suspends after 30 minutes, even when I am active with mouse and keyboard. My logind.conf:

[Login]
HandlePowerKey=suspend
IdleAction=suspend
IdleActionSec=30min

My Ubuntu 15.04 setup is very minimal, and I would like to keep it that way. I login at the console (I don't want a session manager) and then type startx, which launches my ~/.xinitrc that executes i3, my preferred window manager. I do not want to use a desktop environment.

I want the computer to suspend and lock after a given amount of time.

So, my ~/.config/i3/config file includes:

exec "xss-lock -- i3lock -c 000000"

The screen locker works fine, and integrates fine. So no problems there.

In case it is of interest:

loginctl show-seat -p IdleHint

Yields:

IdleHint=yes

Seems like that should be "no" if I am active, right?

And if I do this:

gdbus call --system --dest org.freedesktop.login1 --object-path /org/freedesktop/login1/session/c1 --method org.freedesktop.login1.Session.SetIdleHint false

or this:

dbus-send --system --print-reply --dest=org.freedesktop.login1 /org/freedesktop/login1/session/c1 "org.freedesktop.login1.Session.SetIdleHint" boolean:false

Reading IdleHint still outputs "IdleHint=yes"!

So what am I missing? How do I keep systemd-logind from suspending while I am active, without using a session manager or desktop environment?

I know that I could use lxqt-powermanagement, for instance, but I think I am correct in assuming this is unnecessary. Of course I can change my personal preferences regarding desktop environment, and will if necessary. This problem seems solvable, though.