Why an outlet tester light blinks?
The light is probably not an LED, but it is a neon bulb.

Neon bulbs get old and they will light only when there is outside energy available to excite the gas inside the bulb. This outside energy is light.

You can also see the effect on old power bars that have an illuminated switch that constantly flickers.

If you use the tester in a dark room, the bulb will probably not light.
It will probably light if you shine light onto the tester.

The solution is to replace the tester.