Marking exams can be long, boring, and un-engaging.
It is important one remain focused though to ensure that the evaluation is fair to each student.
What are some methods one can employ to maintain focus and not zone-out while reading answers?
There is two issues in your question.
My own policy is the "mark-one-question-and-shuffle" : I correct the first question/problem for all the students, then I shuffle the whole stack and go for another question that I also pick at random. This way if I am tired or in a bad mood, it will impact everybody, so it will be fair.
I cannot answer to that and I guess it depends of many personal factors. Personally, I find marking tasks boring but easy to do and easy to focus on. It's like driving, some people can drive for hours, others can't. To tell the truth, marking is somehow relaxing for me.
I suspect my answer will be less applicable to math (your subject) but your question is not specific so I'll cover my subject (business management).
First, I find the more I can process in a single session the more fair my marking is overall. In my field, answers are not so clear-cut. That is, there is rarely a right and wrong answer but rather the process of application/evidence that is evaluated. Because of this, there is a risk of being inconsistent when marking in different sessions.
Second, I try to process 10 or so exams before actually marking any of them. The reason for this is that I need to understand the general level of the group. If I don't do this, I find that I am much stricter on the first few exams and get easier as I find everyone is at a lower level than I had anticipated.
Third, I try to give my eyes a break between exams. That is, stare at a point some ways off so that my eyes are not constantly focusing on a point to close (which causes strain and can cause lasting problems).
Your own website says:
My primary area of research is the application of mathematical methods to educational testing
so I'm sure you have much more experience (first-hand or second-hand) and have given it more thought that you let appear in your question ;-)
Of course, it heavily depends on the type of examination being marked, but unless it is very short, I tend to simply split it into many short bursts, and do those at a time when I am well rested (morning) and when I am outside my regular “work” setting: public transportation, waiting room of a doctor, café, in a garden when it's sunny, etc. The mood of the place I'm in helps, and gloomy settings just get me bored faster.
True story: a bottle of wine (well, maybe just half a bottle). Spirits are not a good choice since they go quickly to your brain.
Sorry if I hurt feelings with my answer but the truth is that this technique is more common in the academia than I would like it were.
Another technique consists of splitting the marking into several short sessions.