I have measured LBC horn currents once or twice in the past; not TR4 horns, but ones that were similar. They always seemed to be around 10 amps each, so you will need at least a 20A fuse. I would make it 25, just to have a little margin.
The fuse specs in the owner's manual are for original wiring. You may not have that, and may not have original types of lights and horns and may have additional electrical stuff. The fuse ratings may have to be changed accordingly.
Wiring sizes for your home specify #10 wire for 30 amp circuits, #12 for 20 amp. But those are very conservative, for obvious reasons. Once, as a test, I put 10 amps through a foot of #20 wire, and while it got a little warm, it was in no danger of melting its insulation. I think that's why auto wiring generally has smaller conductors for a give circuit; it just doesn't have to be so conservative. You won't start a fire by putting 20 amps through a piece of #16 wire.