After a lot more effort than should have been required, I finally identified the coordinates of this last AVIA VOLT station.
There are press pictures of the station on AVIA VOLT website, but they never say where it was taken.
The Frauenfeld station is not mentioned anywhere in any text or communication on their website. It's also not visible on the map of all charging stations at https://aviavolt.ch/card/ nor in the list of stations to pick from on the ad-hoc payment page https://aviavolt.payment.longship.io/ Maybe it's under the "show more" button that doesn't do anything? It does show up after you search for "Frauenfeld".
It's however visible in Swisscharge roaming data. But it wasn't showing up when I was using the search feature of Swisscharge.
It seems like Swisscharge has a fixed tariff of 81ct/kWh for all AVIA VOLT locations. However not all stations have the same ad-hoc price. This one shows 65ct/kWh on the ad-hoc payment page.
I was able to locate the station from the video of the photoshoot published in July 2023 on Facebook https://www.facebook.com/reel/241781975293716 , where we see Automobile Kauth in the background.
The earliest picture I can find are on the car wash marker on Google Maps from May 2023. We see the chargers are already installed in the background of one of the pictures.