I've had a problem with a Speedmaster, which shares the same exact harness as the America. A problem that Triumph has had is the connectors pushing out of the fuse box. They look ok when you view them, but will make intermitant contact, causing you to go nuts at times.
I've replaced one harness on a bike under wnty, and ran an inline for the main power fuse on one that was no longer in coverage.
Remove the fuse box from it's mounts and see if you have a loose connection.
Pete