Electrical – 555 timer based PWM fan controller does not PWM

I notice from your circuit that the 555 and motors are running from a common (5V) power supply without any form of decoupling. The 555 is a current hog and draws a surge of current from the supply every time its output changes.

Try putting a large electrolytic (say 220uF) and a 0.1uf (helps with high frequencies) across each the Vcc and ground pin of the three 555s.

I would also make the capacitor at pin 5 a bit bigger (say 0.1uF) - its job is to smooth out any noise of the internal divider chain of 5K resistors. 47pF is way too low.

You should tie the /RESET pin to Vcc. If you have a CMOS type this can keep it from working.

Pin 5 may be optionally connected to ground through a 10nF capacitor, but leaving the pin open will not keep the circuit form working.

Your power supply needs two connections (only one is shown connected in the above schematic), but it should not be as high as 8.4V. The module specifies no higher than 6V. I suggest an LM7805 regulator to give you 5.0V if you don't have such a supply available. It's not clear whether excessive input voltage would damage the module, so I would avoid it.

The circuit you show will allow the average light to be varied from mostly on to around half brightness. If you want more range than that, it's better to use a couple diodes with the circuit. If you have the CMOS type there is an even better way to connect it- leaving pin 7 open and using the output. You can test the 555 output with an LED and resistor to GND- it should vary the brightness- before connecting it to the module.