Hi,
Also, regarding resistive divider supply voltage, it might be of help to place a 10nF to 100nF capacitor across each resistor.
What is the PNP feeding - is it literally an LED, a high impedance input pin, a current-driven or current-heavy load or what?
For 13.5Vsupply down to 8.5V to 9V, a 3V dropout 7808 or 7809 would work. That or experimenting with a homemade regulator or a "poor-boy LDO" (as someone else called them). The resistive divider approach on a supply pin with fluctuating input current range is a grim method to be avoided and prone to causing problems with the LM567 functioning correctly, plus must repeat point of bypassing capacitor(s) on suppy pin, as already mentioned.