It really does sound like load on a solenoid, I would probably try the process of elimination and disconnect them one by one til you find the culprit.
Probably not what others would suggest, might be a better way but if all else fails it might be worth a go.
Hope you get it sorted.
Cheers: Brettski... :)
Might be the only way to find it.
Could be just a bad diode??