I only read the book partially so far (and a while ago), so I don't recall any specific advice regarding 'keeping it in front of you'
There's no specific advice on keeping it in front of you. But he does talk about a "Closed List" - ie one that does not keep expanding.
On his 1 page Quick Start Guide - How to get everything done by Doing It Tomorrow just before page 1 of his book, he says :
1. Put all the work that you are behind on in backlog folders (email, paper, etc.) and put it where you can't see it
2. Collect all your incoming work during the day and deal with it in one batch the following day. Group together similar activities like email, paper, phone calls and tasks. Aim to clear the lot every day
3. If anything is too urgent to leave to the following day, write it down on a separate list and action it at a convenient time during the day. Never take even the simplest action without writing it down first.
4. Spend some time on clearing the contents of the backlog(s) first thing everyday. When you've finally cleared them, find something else you want to get sorted and start doing that first thing every day instead.
If you follow this simple process you will be totally on top of new work by tomorrow and you will be well on your way to clearing your backlog.
My take on the above is that :
I need to keep items in 2 above (what he calls a Closed List) "in front of me"
somewhere and what better place for me than the desktop. And that can include items from 3 as well.
And that also ties in with items in 1 he recommends should be "kept where I can't see it"