PeterJoe, thank you very much for your diagrams; they are very helpful. I have got the horn relay wired differently than what you show; so will have to redo that - once I work out the rest.
And Slick, I am using a 20 amp fuse. Any thoughts on that? That is the size fuse the bike has always had. As part of this process I also put a 20 amp fuse into wire that I am connecting to the main circuit at the ammeter, and off which I am powering the relays.
By way of further background I am running a prefocus halogen headlight bulb (and I have installed a Sparx three phase alternator and a Podtronics regulator - not that that should be relevant to this issue; not running at the time of testing). I use a Motobatt 9 ah battery, which I have hooked up to a multi phase charger, so it is fully juiced up when I am testing/using the circuit.
To my knowledge I have not previously had a problem of the fuse blowing when using horn with headlights, but that said I have had occasional blown fuses before with no obvious cause; I wonder if that could have been it. I have always had a problem with an unreliable horn; very sick sounding. I did replace the horn from stock with a cheap little one that I have mounted near the battery tray. The sick horn was temporarily fixed when I fitted the new switch at the weekend, it sounded good and reliable - after a few tries; but interestingly after I had ridden the bike to the testing station to get a new warrant of fitness (new switch fitted; no relays then), it sounded off. Luckily the tester was an old guy who tol me that he has a Triumph Speed Twin, and was sympathetic.
Incidentally I have just bought some new wire at the local Auto parts store (in this case Repco; the other main consumer based auto parts store over here is Supercheap - both Australian chains) so that I can redo the earth wires and make them tidier - by running them all outside the headlamp shell and then joining them and taking them to an earth point; as opposed to trying to connect them in the shell and taking up room that I don't have. The highest amp wire that they had on the shelf was 15 amp - which I bought - does this mean that if I am using a 20 amp fuse I am risking the wire failing somewhere on the circuit? Presumably the rest of the harness would not be rated any higher than this wire? And the wires in my new horn/dip switch are much thinner, and so presumably have a lower amp rating.