so if it works repeatedly with the jumper and not without it...this means the current flow from the battery... through the fuse and any connectors along the way...through the ignition switch to the flash relay has met some resistance due to dirty or corroded contacts!
you need to check all connectors and fuse connection are clean, if you cannot get it to work after doing this then it maybe the contacts in the ignition switch that are dirty...this is an area i am unfamiliar with, i dont know if they can be inspected and cleaned or whether a new ignition switch would be necessary, that one is for you to decide but do the stuff you can do...its late now in uk so i'll check up on you again tomorrow