The opamp is a simple multivibrator, that produces a square wave at it's output. Not sure what the "test points" are for, but if you conect a resistor across the two points, the LED's should flash alternately.
that circuit is actually a diode tester circuit.test points are for fixing that diode.so sir as u said instead of keepig that resistor by placing a diode if it is working led glows rgt?