That module is based on the common BISS0001 PIR sensor IC. That specific module is not common, especially with 4 pin outs, but since the IC is the same, it all applies.
The On Time, Off Time, and Trigger Mode are handled by a few pins on the IC.
On Time is handled by pin 3. The resistor(s) and capacitor connected to it determine the time. The Formula is
Tx in Seconds ~= 24576 * Rx in kΩ * Cx in µF * 0.001.
Off Time is similar, and handled by pin 6.
Ti = 24 * Ri * Ci * 0.001.
Most Likely, Rx is R14 while Ri is R13, on your board. Cx is C9 and should be 0.01 µF, while Ci is C10, and should be 0.1 µF. Check with a multimeter or magnifying glass, it shouldn't be hard to trace this circuit.
Next is Pin 1, A (Trigger Mode). If connected to Ground/Low, it will not retrigger while it has already detected motion, It ignores further movement until the IC goes through it's On AND Off time. If connected to VCC/High, it will retrigger, so it will restart the ON time. It stays on until movement stops.
If you want to use the module to just detect movement for you, on a quick read, you need to do 3 things:
- Change Rx to a lower value. Something like 1kΩ should give a 0.2 seconds On Time.
- Change Ri to a lower value. Something like 100kΩ should give 0.24 seconds Off Time.
- I recommend setting the Trigger Mode Low, so that it will only detect motion once every (On Time + Off Time). If it's set to high and continues to detect motion, your Arduino will need to figure out that it's continuous motion instead. More logic.
As for the CDS Pin, a CDS is a Photoresistor. A photoresistor is typically used to bring pin 9 Inhibit low when there is sunlight. It's normally used as the lower part of a voltage divider. Why it's changing state when the module detects motion is WEIRD. This means it's either wired to something else, there is a short or break in the module, or it's mislabeled. You will need to check the circuit for it. Here is a general schematic for these types of modules, but not your specific one, for reference.