PieterP:
Or you could just use a monostable 555 timer, no need for an Arduino.
Or double the value of capacitor C6 on pin4 of the BISS0001 inside the PIR.
That will double the 'stay on' time of the PIR, controlled with the 'time' pot, for up to 14 minutes.
No need for any external chip then.
6v6gt:
...there has also to be an LDR or similar light sensitive device to ensure the light does not come on during daylight.
There are two pads/vias for an LDR under the dome of a common HC-SR501 PIR.
They connect to the enable pin9 of the BISS0001. With LDR, here is no PIR output when it's light.
The PIR output can directly drive the base of an NPN transistor (no base resistor), that can switch a relay.
Several PIR sensors could drive that transistor with a diode 'or'.
But where's the fun in not using an Arduino.
Leo..