Accessory mascots were not generally approved by a manufacturer and were often fitted to vehicles that did not have a factory fitted mascot. Sometimes owners would replace a factory mascot with an accessory mascot more befitting to their own personality.
Also, as motometers were gradually replaced with in-car temperature gauges accessory mascots were often fitted to the radiator cap in their place.
It is fair to say that accessory mascots were often made from better materials than factory mascots. Many accessory mascots were a straight copy of a manufacturers own design, an example of this is the beautiful 1933-1935 Buick goddess. Sometimes the copy was of a higher quality than the manufacturers original!
Accessory mascots were produced to cover a wide range of interests and hobbies. A horses head mascot, for example, may have indicated the owner's interest in horses. A running fox may indicate an interest in hunting, Etc.
However, this was not always the case. Many accessory mascots really had no bearing on any subject and were used simple to add that bit of style to a vehicle, perhaps giving it a sense of speed. In fact there are many speed nymph accessory mascots which were designed for this very purpose.
Many companies made recognized vehicle accessory mascots, these can be seen in their literature and brochures. However, many of the so-called car mascots were in fact ornaments firstly fitted to ashtrays, clocks, trophies and some were even flagpole toppers!