The Gas company came and checked the Gas pressure and all is well. You're right, they came out right away and wanted to be safe than sorry and they do this free of charge.
The gentleman that came also exclaimed that he's never seen a setup like mine. He did assure me that the control unit I described is in no way connected to the furnace but it could be that the wires go to the furnace enclosure to run the wires to another "motor" unit which controls some sort of a vent. Still strange and I don't understand it.
He did recommend that I clean the furnace (normal maintenance) and to call a specialist. That's my next step.