Problems with Conversion of 1960s era transistor radio to a guitar amp
A rod piezo (or any piezo) has very high impedance: it puts out a good voltage signal but at very tiny currents. It will not be able to drive the common-emitter input stage of that radio's audio amplifier.

You would need to switch to a magnetic pickup, or add a buffer stage so this amp does not load down the pickup. A common simple circuit is to use a JFET preamp.

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This was from http://www.till.com/articles/GuitarPreamp/

This is a very common circuit and used for things like buffering a condenser (aka electret) mic capsule to drive a standard audio input.

Essentially no current is taken from the signal input since the junction is back-biased. The JFET converts the signal voltage into a modulated current through R3.