Welcome to the forum
As you found, when reading empty it still had just under 1/3 tank full. There are 4 sensors mounted to the sides of all your tanks. The bottom one is ground and the other 3 are positioned on the sides at the appropriate “level. As you add liquid, the “resistance” changes and that’s what makes the lights illuminate. Try putting 9 gallons back in it and then rock the trailer. It might cause the 1/3 light to blink as the water makes continuity with the ground and 1/3 sensor.
That said, there are more accurate systems that can read in 10ths but that’s more $$$.
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2012 Copper Canyon 273FWRET being towed by a 1994 Ford F350 CC,LB,Dually diesel.
Airlift 5000 bags, Prodigy brake control, 5 gauges on the pillar.Used to tow a '97 Jayco 323RKS.
Now an RVIA registered tech. Retired from Law enforcement in 2008 after 25+ yrs.