Ajstoner 21
All the red flag on the typical GA turn cordinator tells you is the instrument is recieving power. Since most failures are caused by a failure of the instrument gyro motor the flag will still disappear because while the instrument is recieving power but the instrument will not be functioning because the gyro is not spinning up.
As was pointed out (before the thread diversion into the legalities of back up instruments for IFR flight operations ) a functioning turn Coordinator is not required in the USA for day VFR flight, but if it is installed it must be working.
The likelyhood a failed turn coordinator would actually cause a problem is extremely low, but not zero. The best way to handle this is to have an A & P
have a quick look at the instrument, as the problem could be as simple as a loose connection, and if he/she finds nothing obviously wrong pull and collar the circuit breaker and placard the instrument as U/S.
From your intial post I assume you do not own the aircraft. If that is the case your only duty is to inform the owner of the problem. If you do own the aircraft and assuming you are not flying it IFR than I would shop around for the cheapest exchange overhaul from one of the big instrument repair outfits.
You can send in your unit for repair but usually it is cheaper and faster to just get an exchange instrument.