The prewired kit you have bought will work as it is (plug an amp lead into the jack socket and hold the pickup over the strings whilst you strum and you should hear it through the amp - if you don't then check the volume is turned up). It is a ready to go circuit, but often it will give some hum and if this is the case the next step is to ground the strings with one extra wire from the back of the volume pot to somewhere in connection with the strings (so the bridge if it is metal or if not the tailpiece is used and if the tailpiece is also wood put a metal strip that the strings pass through before passing into the tailpiece and solder the wire to this strip).
Thank you for the photo - depending on the string spacing I suspect you will get either no sound from the outer strings or a noticeable volume difference.
When others have used this pre-wired pickup they either position it across so 3 out of the 6 poles of the pickup have a string near them, or slant it at an angle so the strings cross one or more of the pickup poles. As it is a single coil pickup (as opposed to a humbucker) you often find they transmit electrical noise from nearby lights,computers etc unless you also ground the strings by adding another wire from the bridge or tail piece ( add a metal strip through the tailpiece that the strings pass through unless you are using a metal bridge or metal tailpiece in which case solder the wire to part of that) the other end of the string grounding wire is normally soldered to the back of the volume pot which is used to provide a central point to ground all the bits that need it before a single ground goes from this pot to the output jack ( it is supposed to stop ground loops). If you find it hard to visualize what I mean by slanting the pickup just say and I will find some photos to demonstrate this tomorrow.
I'll go into more details about the piezo then.
Are you able to take a photo of the wired pickup or post the link off the www then I will have a better idea of the wiring? I am off to visit relatives until later so will reply properly then.
You commented on difficulty getting parts - I use ebay and get a fair amount from China/Hong Kong. Delivery can be 2 to 6+ weeks but any small problem has always been sorted quickly (also for UK I have to keep below £15 to avoid import tax/duty). The ones I have used recently
page 8 (Les Paul type) or page 11 (telecaster type 3way).
You do not need the same pickups as shown in the diagram use any 2 wire magnetic pup as the neck pickup and your piezo(s) as the bridge pickup in the diagram. If you add a tone (you can just omit it from the schematic) note it will have no effect on piezo tone.
The other options are a blend pot, or using diodes (for a first go the above will be easier)
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