For starters, that is a very poor layout of a timing crystal circuit.
"The circuit board was designed by a perfectionist with an eye for simplicity and elegance."
The designer might be meticulous about simplicity and elegance but knows little about proper electronics design.

The quartz crystal X1 ought to be connected to pins 17 and 18 of the PIC16F84 MCU chip, along with capacitors C6 and C7.
These are located too far away for the proper pins. This can be the reason why the adjustment is ineffective.There is nothing you can do about that. (I know, you said that you are not an engineer, just a clock owner.)
The photo confirms that the trimmer is a trim cap C7 and not a potentiometer. The information the seller has provided you contains some inconsistencies.
Still go ahead and do the 24-hour tests using a ¼ turn of C7. Let us see your test results.
"The circuit board was designed by a perfectionist with an eye for simplicity and elegance."
The designer might be meticulous about simplicity and elegance but knows little about proper electronics design.

The quartz crystal X1 ought to be connected to pins 17 and 18 of the PIC16F84 MCU chip, along with capacitors C6 and C7.
These are located too far away for the proper pins. This can be the reason why the adjustment is ineffective.There is nothing you can do about that. (I know, you said that you are not an engineer, just a clock owner.)
The photo confirms that the trimmer is a trim cap C7 and not a potentiometer. The information the seller has provided you contains some inconsistencies.
Still go ahead and do the 24-hour tests using a ¼ turn of C7. Let us see your test results.


