Thanks Moggy!
This confirms that the Sweet Talker controls the /WAIT line to introduce delay during speech processing. The yellow circle contains the trace that is connected between your resistor-transistor network and the /WAIT input to the ZX81 (pin A19 on the connector).
The network likely uses an RC circuit to hold /WAIT low for a period of time. Changing the resistance will change the rate of voltage decay on the network, causing the pulses on /WAIT to be shorter or longer, speeding speech up and slowing it down.
Although using /WAIT works on the ZX Spectrum, it's a dangerous game on the ZX81 due to the negative effects on both video synchronization and DRAM refreshing of introducing wait states.
In contrast, the Parrot doesn't touch /WAIT. Instead, it allows the software to poll the I/O port to detect the completion of a speech command, which works well on the ZX81.