Let us make the assumption that the 32768Hz quartz crystal is running fast.
Get a 5-30pF trimmer capacitor. It might look something like this:



You will solder it in between one of the crystal terminals and ground.
You will have to experiment with which of the two leads works and how to set the trimmer.

The idea is all 32768Hz time keeping crystals are cut to run at a higher frequency. They are intended to be used with trimmer capacitors in order to trim them to the correct frequency. Quartz crystal oscillators are nominally better than 50ppm. You just need to trim them in-circuit.

 

We don’t know whether it even has the capability of using the line frequency or if it is using line frequency but getting errors due to noise. If you can find a schematic, maybe we could help .

 

We don’t know whether it even has the capability of using the line frequency or if it is using line frequency but getting errors due to noise. If you can find a schematic, maybe we could help .

My guess reading the manual is it uses a simple 3.0 volt CR 2032 battery to maintain time when not connected to mains power or during mains power outages. Based on that my guess is the clock has an internal oscillator. Yes, you can try adding a trimmer and another guess is the tiny cylindrical part labeled X1 on the PCB is the crystal. The 32,768 Hz is likely the clock frequency. The crystals cost about $0.30 Digikey. Less a good frequency counter good luck trying to trim the clock. After each tweak you will need to wait for the oscillator to stabilize so less a good means to measure frequency this can be a long process just hoping to get it correct.

The Manual.

If you want an accurate clock there are plenty out there to be had. All things considered what you have likely meets whatever Sony expected it to meet. This is not quite like a temperature controlled crystal oven oscillator, it's an inexpensive clock radio.

Ron

 

If the error is one second in 24 hours that is one part in 60 X60 X24/day, which is fairly good. But if it is an 8 MHz crystal THEN IT IS NOT THE TIME BASE CRYSTAL.
And if it is not using the mains frequency as the time base, it actually might use a crystal time base so that it can be used anywhere in the world.