We have found these IR flashlights to be useful for testing eye tracking setups or even using them as permanent illuminators. They are very powerful (5W). Compact. And have variable focus.
940nm IR Flashlight Single Mode Zoomable Night Vision Light for Hunting
They are powered by 3 AAA batteries. But that can be replaced by a 5V DC power adaptor such us :
These cables are very helpful to build
The goal is to have an illuminator that can be plugged into a power outlet like this:
Pass the cable through the hole before soldering!
Solder the cable that goes to the power brick as shown in the picture. There are other ways, but this requires least modifications and keeps the functionality of the back button.
Push everything back together and close the cap