I've been lucky enough so far in that I've not as yet had a GT where the top part of the gear indicator system has been a problem. I have had a few where the lower engine based unit has had issues with specific gears or digits not working on the LED.
What I have found has been problems caused by a combination of brittle or broken wires on the unit attached to the engine, and on one occasion the unit inside was worn and dirty. I guess this shouldn't be a surprise considering the bikes are over 40 years old and that Suzuki had mounted this unit directly next to the front sprocket.
Dirty job this, with all the accumulated oil and junk from the sprocket picked up from the roads all baked up together over the decades. Need to try to clean away as much of this accumulation as possible and under there are a bunch of wires and electrical contacts.
Once clean away, the unit can be taken off by removing two screws which bolt it to the crankcase. Picture below shows the unit cleaned up and waiting removal.
See how close the unit is to the sprocket and how much hot crap the electrics have had to deal with!
I've encountered two slightly different versions of this unit so far. One is an all metal and the other plastic. I've added pictures of both types further down.
The unit is simply a set of electric connectors bridged based on a key driven off the engine block.
Depending on which gear the bike is in, the key is in a different location and that makes a different digits come up.
So far I've been lucky and the issues are fairly obvious once you get the unit off and inspect it and been limited to failed wires or crap having got into the unit and preventing proper electrical contact.