You have a failed connector
It could either be the MagSafe “L” connector attached to the cable/power brick or it could be the MagSafe to MagSafe2 (MG to MG2) adapter.
The tell tale sign is that LED should never come on unless it’s connected to the DC-in board of the MacBook and successfully communicates. MagSafe chargers use the 1-Wire signaling to communicate between the DC-in board on the Mac and the chip inside the MagSafe connector.
This is what turns the light amber when charging, green when fully charged, or flashes when there’s a problem. The fact it’s happening when the connecter is disconnected means the problem is with solely with the connector end and not the Mac.
There is an excellent write up entitled Teardown and exploration of Apple's Magsafe connector that goes into further detail on this topic. It’s worth the read.
Possible Fixes & Diagnosis
- Remove the MG-MG2 adapter. If the LED stops flickering, it’s likely the adapter has failed. It’s easy and inexpensive to to test by getting a replacement
- Clean the contacts on the “L” connector and both sides of the MG-MG2 adapter. Use 90% isopropyl alcohol (IPA) and not the normal 70% you get at the pharmacy/chemist. You can use a stiff nylon brush (like a toothbrush), but just don’t use water. Allow the IPA to evaporate completely before using.
- If the LED continues to flicker after removing the MG-MG2 adapter, you might need to get a new charger.
Remember to unplug from mains before doing any of these services!
Further Reading: