If you use a PIR sensor, then you might not need an Arduino.
Common PIR modules can work on 12volt (buildin 3.3volt regulator), and have a time delay pot (~0-7 minutes).
All you need is a mosfet to switch the LED strip with the 3.3volt logic signal of the PIR.
The hard part could be mounting the PIR so that it's only triggered when you want it.
Leo..