The controller board is under the cover with the white and yellow stickers.
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Before starting I unplugged the AC power cord and opened the battery disconnect. I then unplugged the red/brown spark electrode wire and the two 12V DC pins. The 120V pins were on really tight so I used a screwdriver to gently pry them off after I dismounted the board.
The upper left and lower right screws hold the cover on and the other 2 attach the board in its plastic base plate to the wall.
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Once the board is out on the table, I removed the plastic rear cover. The AC relay is the one here. It can be confirmed by looking at the back side of the board. One of its pins connects to one of the AC input pins and another goes to an AC_HT pin.
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The replacement relay cost $2.05 but shipping added another $3.75. Here's the new relay next to the old. I got it here:
http://www.digikey.com/product-detail/en/G5LE-1A-E-36%20DC5/Z5217-ND/1815659
Now installed on the board. It's a de-solder/solder job but only took 5 minutes.
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I reinstalled and reconnected. The fridge ran perfectly on AC for 4 days so I'm declaring victory, for less than $6. If I just got lucky and it acts up again, a new control board is the next option.