That 10 gal gas only should be a G10-3E version
Brown wire is 12VDC POS from battery to the on/off switch
From switch to/thru Thermal Fuse -- to/thru T-stat and then to Circuit Board (top pin on the 6 pin connector)
When T-stat closes ,,,12VDC POS goes from Circuit Board via RED wire (4th pin) to/thru ECO --- to Gas Valve solenoids to Ground
12VDC NEG ...Bottom pin to battery Neg and chassis ground
****Check that you have GOOD Grounds
TO TEST POWER TRACK:
Place negative lead of the multi-meter to ground (green wire) track of edge connection and positive lead of the multi-meter to top power (brown wire) track of edge connection.
*If no continuity, board is defective
TO TEST VALVE TRACK:
Place negative lead of the multi-meter to ground (green wire) track of edge connection and positive lead of the multi-meter to valve (red wire) track of edge connection.
*If no continuity, this indicates a blown valve track.
GAS Wiring is top diagram