If it's new and it doesn't work out of the box, it's faulty
If you take it off, and experiment a bit ... hold the body and push the lever up and down ... you will see how it works.
There's a whole complex spring loaded mechanism in there. When you put the lever down or up, you will see how the plastic tab in the middle pops out? That contacts the steering column - when you have the lever off you'll see what I mean. The column is cut like a gear, to catch and flip that little bit of plastic.
If the lever is working as it should, then it comes out the same distance whether the lever is down (turning left) or up (turning right).
When turning left (lever down), simulate the action of those gear teeth on the steering column by flicking the plastic bit that sticks out down. The indicator lever should stay down. As soon as you "turn right" i,e, flick it UP, it should spring back to middle position.
Opposite for lever up (right turn); it should stay on while the lever flicks up, and cancel when it flicks down.
If that doesn't work ... it's faulty.
Don't try taking it apart. I did and all I ended up with was a mess. Luckily, I'd bought two. I managed to break the horn wires on the first one. Lesson number two - don't try to tidy any wires on it that you think shouldn't be sticking out where they are
edit to add: I am assuming you did screw it back in tightly. Not having it screwed in properly would also give inconsistent operation...