Typical G6A schematic
Looking here, the 12V on the 'blue' wire is for the lockout light. I assume that works?
Now disconnect the 'red' wire to the ECO sw. and the wire to the 'spark & sense' and try connecting the brown to positive, or if you are low on fuses, place the ohmmeter leads on the 'brown' and 'green' wires to see when the "short" disappears. A short will show as less than 25 ohms let's say. Also some circuits matter if the red/black meter leads are one or the other wire, so try both ways (Red meter lead should go to the 'brown' wire.)
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