I have a CF653C-H Cozy wall gas heater ..The fan runs fine , except when it shuts down , it clicks 15 to 20 times before stopping . At least I am guessing its the fan, could also be the motor ..But there is no issues during the normal run.
If the wall heater is very old, the motor could be a split phase or capacitor start motor with a start winding switch. Sometimes when these motors get worn the start winding switch will make noise that is noticeable when the motor is coasting to a stop. It could also be worn motor bearings which can be checked by moving the shaft up and down to see if there is any up/down play. By checking the replacement parts list I see that the replacement motor has a different model number than the original which usually indicates an older unit. If it is the switch that is making the noise that does not mean that the motor is worn out, it's just worn.