First, change the LED drive to a common emitter as follows:
This will invert the sense of the LED ON/OFF relative to U1F. An inverter can be put in series with U1F to restore the original sense.
Change the supply voltage of the 4069 to 3.3 volts, same as the R-Pi, or use the R-Pi's power supply. The LED drive voltage can still be the 12 volts.
Connect the GPIO port to the junction of U1A, R2, and the switch through a 1K resistor as shown. This will limit current through the GPIO port id the switch is close while the GPIO pin is an output.
Use the GPIO pin to control the toggle function as follows:
The pin is configured as an input.
Read the logic level on the input.
3A. If the input is high, change the pin to an output with a logic low, wait for the signals to propagate, then change it back to an input.
3B If the input is low, change the pin to an output with a logic high, wait for the signals to propagate, then change it back to an input.