So I got a replacement dock. Now we don't have to press on the dock to get the LED to come on (or stay on).
Unfortunately the gTar and the phone still don't pair. This is iOS7 in the video, but even before the upgrade the behaviour was exactly the same.
Turn on gTar
Turn on phone
Open gTar app
Dock phone into gTar, nothing happens.
We have also tried opening the app AFTER docking. That doesn't work either.
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