Sorry, have just re-read your opening post and realise you have already done that check, at least that is one thing it isn't but I would also do a continuity check from the unit to the ICU to rule that out as an issue as well.
Re the oil and fuel level warning lights, are you getting 12v on the red/ black wires? This also feeds the advance unit as well so an issue here may explain both problems?
If you do then have you checked the diode block?
Regarding the 12V on the red/black wire, I've never tested it
I think I do because if the ignition toggle switch is on the off position and I try to crank the engine, both bulbs light up as they should.
The diode block is that rectangle made from some kind of hard resin under the seat with an plug on it?