That's not a patch repair, the suggestion suggests customer wants it done on the cheap. If repair section available then not too bad a job providing you get to good metal eventually.
Wet the area then observe the reflection. When filling, the usual mistakes is to rub down too much....in your case you're going to need filler over and beyond the high spot....unless you intend to remove the high spots.
Sounds like you want the socket behind a wall mounted TV - in which case down from the top probably isn't as bad as you might think. Remove plasterboard at noggins and drill through. A lot will depend on what access is like from the top.
Old gravestones used to have lead poured in the characters, you'll often find them on the ground around the base as the stone crumbles - a few holes drilled at odd angles helps retain them.
Gold leaf would be an option.
I had a print going this afternoon in black resin so threw a few of these on the bed, scaled the original 15mm diam by 66% to get 10mm...
Print was fine except for one small area.
I was thinking something like this and fill with either clear resin (if your backlighting is permanent and you don't want the symbol visible in ambient light) or translucent white resin if you do want it visible in ambient light...