What you've circled there appears to be the indicators, not the sidelights. The sidelights are the tiny twinkles in the headlamps, which should stay on with the headlamps as standard.
When you put the lights to just sidelghts, you should get just the little twinkles at the front, and the tail lights and number plate lights at the back. Then the next switch position adds the headlamps.
If the amber lamps are lit at any time other than when you are indicating, there is a fault, probably a bad earth, that needs finding and fixing. A bad earth at the rear lamps is favourite, and can affect the front lamps as the current goes the wrong way through any circuit it can find.
You do not want the amber lights on in normal driving. This would contavene lighting regulations, and make turnign less safe. Having one flashing as a signal, while the one the other side is still on will not show the message you need, and others are likely to not see, or ignore the flashing one. You would also lose the alerting affect of it coming on when you signal, as instead you'd be turning it off first, not on.
