If it's the same as the circuit in the .zip file linked elsewhere in this thread, then it's not a ring modulator, it really is just a chopper.
Have a look at the circuit diagram. IC4 is an oscillator and binary counter, which has four outputs which are buffered by the transistors and fed to the switching inputs of IC3, a quad analogue switch. The outputs can be independently switched on and off, and fed to the mixer comprising RV2, R25, R26 and IC2b and friends.
The distortion part is is IC2a, the resistors around that, and D2 and D3 to do the actual clipping.
Last but by absolutely no means least, IC5 and IC6 are the echo chip and its memory. It's used as serial memory, so don't expect too much from bending it. You might be able to do something clever with RV4, to wobble the delay time. Break into the circut around RV3/R30 to mangle the feedback loop - possibly adding a pitchshifter here to get "fairy dust" effects.