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Use 1/4 of 324 in "comparator" configuration - see picture below ..
Time dalay of a RC circuit can be calculated as follows:
t = R(in Ω) * C(in Farads)
Try to use R1 = 1MΩ and C1 = 2.2µF, and with Ra and Rb set the level at ≈80% of Vs (supply) .. this should give you ≈1s delay ..
For Ra=10kΩ (100kΩ) and Rb=39kΩ(390kΩ) the 80% condidtion will be true for Vs=8V, but it won't be true for Vs=12V ..
If you would like to make this circuit independent of the Vs voltage, wire 1kΩ resistor in series between Vs and (Ra+Rb<->R1+C1), and an 8.2V zener diode in parallel with (Ra+Rb<->R1+C1) ..