How to tighten SRAM HRD Rival brake lever? I have SRAM Rival HRD brake/gear shifters on my cross bike. It's a 1X setup.

The left brake lever (this is the UK where rear brake lever is on the left, so it's the rear brake lever only) has lateral play. The shifter can be wiggled a little side to side and a little forward and backward before the brake starts to engage.

I would like to stop this play, the right hand front brake/shifter lever has no or much less noticeable play. 

Firstly, I know the brake needs bleeding, and I will get this sorted but is there any way to tighten the lever?

I see from the exploded view in the service manual that there is a pivot pin. It doesn't appear that this can be tightened?

Is it likely that simply bleeding the system will remove some/all of the play or is there something else I can do?
It was much improved by a service at a shop where they replaced the brake pad and bled the system. It seems tightening the pivot pin was not needed.