How can I get an indicator icon for new updates?

I logged in this morning and had my updates icon, just as I wanted! Here’s what worked to get this working using commands in the terminal:

1. Check what’s already allowed using gsettings get com.canonical.Unity.Panel systray-whitelist since you probably don’t want to turn anything off. My default value was ['JavaEmbeddedFrame', 'Mumble', 'Wine', 'Skype', 'hp-systray', 'scp-dbus-service'].
2. If you suspect you have other missing icons (for example, Pidgin), you can find the correct values to add to the list with grep TrayChild ~/.xsession-errors ― if something tried to add itself to the tray it will show up with the name the system knows it by.
3. Add update-notifier (and anything else you found in step 2) to the list. If you had the same default values as I did, use this command: gsettings set com.canonical.Unity.Panel systray-whitelist "['JavaEmbeddedFrame', 'Mumble', 'Wine', 'Skype', 'hp-systray', 'scp-dbus-service', 'update-notifier']"
4. Now set update notifier not to auto-launch (this is from the question): gconftool -s --type bool /apps/update-notifier/auto_launch false

Next time there are updates, you get the icon notifying you ― hooray!

I’ve read about Unity hiding some indicator icons so maybe that’s what’s happening here?

If you do not have dconf-tools installed, install it. Run it (from the terminal or from the launcher: if you do not see it when you type dconf in the launcher, check Main Menu settings), go to desktop>unity>panel. Here you have the list of all classes that Unity allows in the systray.

Add your class there, or change the whole string to ['all'] to allow everything.