That you drive a Model S explains why the replacement cost is $257.92. In the Model 3, Model Y it is very easy to access to the 12V battery when the 12V needs to be changed. I believe the price quoted to an Model 3 owner was approximately $135 - $140.I should have been clearer the extended warranty on my 2013 Model S declined to cover the battery which was replaced under warranty March 6, 2017 when the vehicle was 40 months old. My original post states Tesla has declined to cover cost to replace my 12v battery.
My 8 year extended warranty expires December 2021. Was said to cover everything the standard 4 year warranty covered but the documents disappeared from the MyTesla page and I can not find my downloaded copy.
While not Model Y specific, it appears to be universal Tesla policy.