Since refurbishing a magneto professionally can be an expensive proposition, I have included a few tips passed on to me by Brian Pollitt, for checking out your BSA A10 magneto, before deciding to pay for a total overhaul.
Magnetos can be stripped, checked for loose wires, and cleaned inside. It is possible to buy all the bearings and spacers for them separately to repair yourself. You can even buy an exchange armature off the shelf.
The problem of dynamos not working when laid up for a while is normally due to the residual magnetism in the magnet which the field coil is wrapped around not being there. The magnet no longer has magnetism or its polarity has been reversed. The way round this is to fit it to the bike and start her up.
If your regulator is OK and it doesn't charge then you need to flash the dynamo to give some power to the field coil and start it charging. You take a wire from the negative of the battery and just after you have started the bike you touch the other end of the wire to the dynamo body for half a second. If the dynamo starts to charge then the residual magnetism has gone from the magnet. Take the bike for a long run as this sometimes remagnetises the magnet. If not then you need a new magnet or the old one remagnetising.
If after flashing it the dynamo does not charge there is something else wrong and it needs repairing.
See also Electrics