Does that mean with the ignition
off the lights stay on?

The circuit (as built by Triumph) will turn those lights on in any ignition switch position other than OFF (remove key postion). If they stay on with the switch in OFF you have done something Triumph didn't intend (with good reason). If you follow the schematic you'll see what ignition switch positions apply power to the yellow wire for the small lights (basically ALL of them). That includes the kill switch. That's the red/orange wire coming out of the ignition switch (sayeth page 18.23 of my manual) that goes to fuse 10.