need help in wiring an vintage circuitry from an P-Style Bass from 1968

It's not a mistake. It does not matter what order the tone pot and tone capacitor are in. Both wiring schemes sound the same.

 

Installing the tone cap between two pots is another common guitar wiring. In every case, one leg of the cap should be connected to the tone pot and the other leg should be connected to ground. So, you can connect the ground leg to the tone pot body or the volume pot body or the ground lug of the volume pot.

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This is uncommon. Are you sure the cap is connected to the middle lugs?

 

The reason the tone cap went from being soldered between two lugs to being soldered and grounded to the tone pot was supposedly motivated by the concern it could get damaged if one of the pots worked loose and turned.

Even though the physical wiring looks different, from an electrical perspective, both ways to physically wire it still give you the same electrical circuit. That's why wiring diagrams don't tell you the whole story. You want a schematic diagram for that.

 

If you want to keep it as original, it's better not to experiment on the original parts. Keep the original controls as they are. Buy new pots, a cap and an output jack and try the standard control setup and see it's better or not.

If I see it correct on the photo, it's not the same circuit. It might sound the same but the circuit is different.

 

The wiring may be different. But it's still the same RLC circuit. Basically you have a signal from the pickup going into a 2nd order lowpass filter. There are a variety of different ways to physically wire up such a circuit. But they're all equivalent (i.e. the same) electrically.

Looking at a photo for differences in physical appearance isn't going to make any electrical difference. The physical wiring isn't the same thing as the electrical circuit.

 

I wasn't talking about the physical differences or the physical wiring. I see a different circuit on the photo posted by the OP.

The standart tone control circuit has the tone pot between the vol pot and the tone cap (the other leg of the cap is grounded).

On the OP's photo, I see the tone pot is between the tone cap and the ground (the other leg of the cap is connected at the output).

As I said, it might function the same, but those two are not identical circuits. If you draw the scematics you'll have different circuits.