The location of the earth on the steering column bracket is behind the instrument cluster that houses the speedometer. But I would not expect a problem with the earth just out of nowhere.

The modules I mean are indeed a sort 'mini ECUs'. On a 90-93 Sierra I believe the door ajar-module is clamped to the backside of the panel where the small glove compartment is on the driver's side and is easy to reach. The lamp check module is mounted high on the bulkhead behind the dashboard on the passenger side and is quite difficult to reach. But I could be that the modules are in opposite locations.

I believe the door ajar module supplies power to everything. So if that one is broken I think the whole system no longer works.