After OG's suggestion of an ignition switch earth I would say it is an earthing problem somewhere else. The trouble is, where! I am not sure how many safety earths the bike has but things like, clutch, sidestands, kill switches all could affect this. I would disconect all of these first. check and clean the earth to coils and CDI and see where that leaves you. You have checked the pick up coil so the ignition (HT) coil(s) should be checked for Primary and Secondary resistance and then that leaves the CDI.
My SV sits outside in all weathers under a cover.