It's a unique piece of history and I think it should be restored. At first I thought it would use pulsed ultrasound to measure metal thickness, as is frequently done nowadays, but that would necessitate a lot of complexity. It's obvious that they used swept CW ultrasound and the motor driven variable tuning cap is a big clue.
So how do you measure metal thickness using swept CW ultrasound ? Imagine the material as a quarter wave open circuit transmision line then at some frequency it will look like a short and at the transmitter end and you can detect that as a sharp null response.
For example, say you have a piece of stainless steel about 1/16" thick and you do a sweep and see a dip at 1MHz. At 1MHz a quarter wave will correspond to a 250ns delay and because ultrasound propogates through stainless steel at 5800 m/s then in 250ns it will traveled 1.45mm.
You would probably only need a single PZT transducer and you can find the 1/4 wave nulls using a VSWR detector or even simpler, just detect the transmitted amplitude. EDIT: I forgot to add that you would also have to compensate for the line length somehow.