Follow the circuit along with the datasheets.
556 datasheet: https://www.ti.com/lit/ds/symlink/na556.pdf?ts=1626711212149
L293D datasheet: https://www.ti.com/lit/ds/symlink/l293.pdf

Shaker part: The 556 has 2 independent 555 timers, one used for PWM control (speed control of the motor), the other one used for setting to and fro timefor the motor.

The U1A of NE556 in the schematic is for the PWM control. It uses the popular pwm control circuit with 555 timer. It has 2 1n4148 diodes along with the potentiometer, varying the potentiometer causes to change the duty cycle by changing the charging and discharging times of the capacitor. Standard PWM frequency can be used as 50-100Hz. The calculation for the same is also attached in the picture attached in this step.

The U1B of NE556 in the schematic is for changing the to and fro times. The 2 diodes here provide the fixed 50% duty cycle, which is essential since to and fro times must be equal and uniform for efficient shaking of the etchant. So by varying the two resistors (essentially dual ganged potentiometer), we can change that time. Do note that whatever be the on-off times, duty cycle is always maintained as 50%. The total time period can be as long as 3 sec. You may change R C values to get different time periods. The calculation for the same is also attached in the picture attached in this step.

The motor driver used is L293D. Only one channel is used. The PWM output from U1A is fed into the EN (Enable) Pin of a channel. Now to feed the 2 control signals, we need an inverter to get complementary signals. So the output from U1B is inverted using a npn BJT configured at the saturation region in common emitter mode of operation. Therefore we get the two control signals. It does not matter which signal you're feeding into which control pin of L293D, as long as the two signals are complement of each other it will work just fine.

Turntable Part: Now turntable mode is a simple mode of operation where the motor will run continuously in one direction. For that the control signals must be fed accordingly. For example, if inputs 1A & 2A are given as 1 & 0 and motor is running clockwise, then by setting 1A & 2A as 0 & 1, motor will run anticlockwise. To change the direction (clockwise or anticlockwise), I have used another BJT as an inverter and a simple SPDT(single pole double throw) switch can help us to set the inputs to the L293D as shown in the schematic.

A simple DPDT (double pole double throw) switch can be used to switch between two modes. This switch will just simply switch the control inputs to the L293D, either to be set to turntable mode or shaker mode, as shown in the schematic.

Now the motor I have used is a 12v DC motor whose minimum operating voltage is 9v, it cannot run on 5v. But the L293D Vcc1, EN and the control inputs supports 5v logic. So that's why a L7805 regulator is used, so that it can supply 5v to the 556 to get 5v logics which is compatible to the L293D as well as feeding the Vcc1 of L293D to 5v.

Supply capacitors are very much important. For 12v rail, 1000uF is necessarily be used (or higher) to deliver ample surge current for the motor. For 5v rail, a 100uF and a 100nF are sufficient,

A red LED is used as a power indicator.

I have built the circuit on breadboard and tested it. It works perfectly fine. You may observe the video files attached here. I have also used my DSO to test the various PWM and control signals. Do note that we have taken ideal conditions, so we considered diode voltage drop as 0. But in reality 0.6v drop is generated at diodes, thus the actual PWM frequencies and on-off times are slightly different with the theoretical calculations. But that doesn't pose any serious problem and circuit works flawlessly. I can easily switch between two modes and can also change motor speed. I used 8.5v Vcc from two 18650 batteries connected in series. The DC motor used is a 12v 60 RPM motor.
For building the platform and supporting structure, I have used mechanics lego toy parts. You may use wood or anything else, whatever comes inside your creative mind.

I have used Kicad software to make the schematic and PCB. Then I used toner transfer method using cloth iron. And the very first PCB which I made with this shaker circuit is this circuit board itself. For this, I have used the breadboard circuit to etch the PCB, then dismantled the components from breadboard, drilled holes and soldered onto PCB. Attached switches and hookup wires. Then again I tested with the finally made PCB. The PCB file is attached here.
It was a big success as I achieved both of my purpose using this single circuit that too without any microcontroller.
Thanks for your time in reading this, do follow me for more projects!!!