I must also appologise for seeming like I abandoned you. It was unavoidable as I was called out on an emergency water line breach. I contract with a local CSD to do their water line breaches, breaks and ruptures. When they call I pretty much have to drop everything and go as the majority of the areas water is dependant on the one system.
HVAC guy is pretty close to your problem. As you have a mechanical thermostat, and the system is still operating there is nothing wrong with it. It is also sending the correct signal for the systems condition. That condition is the heat pump part of it has failed. Whether from mechanical failure of a part or from a loss of coolant.
What this does in turn is activate the electric back up heating coils. These are there for just this reason. They provide emergency heat when the units heat pump fails. This, as you well know, kills your electric budget in very short order.
The indicator light is there to advise you of this condition.
Unfortunatly there is little that you can do as as homeowner. Highly specialised tools, and equipment are required as well as state and EPA required certification for proper handeling, and recovery, of the refrigerant.
All in all, HVACguys advice to have a qualified serviceperson come out and have a look at the unit is the best solution.
A word of advice that will keep you in warm comfort, and allow for a long service of your unit is to have it professionsally serviced annually.
HVACguy has put a lot of effort into answering your question. And his repair recomendation was the correct one.
Please accept his answer and not mine. He has earned it.
Best regards, XXXXX XXXXX Smithy