Mountainman - You are correct in that you do not need a license to get a plate for your motorized bicycle (406a) in California. However, as of 1993, you need an M1 or M2 license in order to legally drive one.
These motorized gas bicycles generally are legal under definition 406a of the vehicle code. They must:
1) Have fully operative pedals
2) Produce under 2 gross brake horsepower and have an automatic transmission (what about no transmission?)
3) Achieve not more than 30mph on level ground
In addition, they must meet older equipment standards (1966 safety standards?) which would mean a mirror, horn, and brake light. And for night driving, also a taillamp and headlamp. The brightness requirements are less than for cars or motorcycles and only single beam headlamps are required. Turn signals may be a good idea but are not required. You are also supposed to have a DOT approved motorcycle helmet.
To get the lifetime plate which now cost a onetime fee of $19, you fill out a form that has a few questions about the vehicle type and send it in. Basically, if it meets items 1, 2, and 3, you get the plate. No inspection required. Most DMV personal and many officers do not know the requirements.
Part of the confusion comes from the fact that California also has a 406b definition for a motorized bicycle:
1) Have fully operative pedals
2) Having a maximum 1000 watt electric motor (about 1.3 horsepower).
3) Achieve not more than 20mph on level ground
No plate is required, there are no lighting requirements, you do not need a drivers license (just be at least 16yrs old). You only need a bicycle helmet.
California has a myriad of confusing, overlapping classifications: bicycles, motorized bicycles (mopeds), quadricycles, scooters, motor driven cycles and motorcycles. All with different restrictions, licensing, and equipment requirements. Each classification does have a particular purpose though many are subject to interpretation. Most of these were done piecemeal and seem to have been tacked on to cover a specific vehicle type. It would be nice if they were consolidated or simplified so that everyone understood them. Even so, they are what we have and at least they are workable and provide a legal means of using these motorized bicycles.