What is going on with the gauges in my mustang? on 2005 Ford Mustang

my 2005 ford mustang, v6, i had to buy a new battery and since i changed out the battery, sometimes the gas gauge would work and sometimes not. Now the fuel gauge is doing the same. I went through the steps of installing a new battery per the owners manusl and it worked for about a half day and back to not working and then working.

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