From what I can see in the pictures it looks like the LED is attached to the small piece of PCB and pokes through a gasket to the outside of the case. The two diodes (with red markings) are oriented to allow current to flow in through one and out through the other (see the reversed polarity bands,) providing an electrical path for the LED and some sort of voltage drop so as not to blow the LED. Since an EFHW has a high voltage at each end at resonance, both the voltage and the brightness of the LED would drop if the applied frequency moves away from the resonance of the antenna. Pretty smart idea, really.
John
VA7JBE