I googled this question and found conflicting advice. Some websites say to avoid eye contact altogether, others say try to make a lot of eye contact. Any security experts know which is the better option?
There may be confusion because in armed robberies suspects don’t want witnesses looking at them and then potentially identifying them later.
In actual hostage situations, anything you can do to make a connection with a suspect is thought to improve your odds of survival and your general welfare. You may wish to research “dehumanization” (although there are probably more technically correct terms in the the psychology literature).
hope that helps,
AZRob
That makes a lot of sense in the context I’m in, actually (bank robbery prevention online class). Thank you!
Need answer fast? 
I remember from my training (also worked in a bank) that you should not make eye contact, but focus on some other part of the body, in order to get a good description. For example, if you can describe their shoes really well, chances are they are still going to be wearing them after the robbery, making it easier to identify them.
Hummmmm, interesting… 
Brief eye contact is probably okay in a hostage situation. A staring contest will probably get you a beating or worse, as it could be seen as a challenge to authority. Eyes downcast: subservience. Eyes locked: defiance.
It may also depend on the kidnappers. Some cultures encourage eye contact, some discourage it. Gender roles can enter into it as well.
DEAR GOD I must have a pair of these. For reasons.
Is there a reason for the glasses looking up and to the left? Looking down is meant to be submissive isn’t it? (Or is that human culture? It’s so difficult to tell these great apes apart sometimes)
For the gorilla I don’t think it matters particularly, what bothered them was that people try to make eye contact. Eye contact is confrontational to gorillas. The woman Bokito attacked was visiting several times a week to stare at him, and thought they had a special connection. Obviously, this is very distressing to gorillas. So looking away, anywhere but in their eyes, would be an improvement. I don’t think up or down matters in this case.
Bank robbers and kidnappers might differ from gorillas. Or might not. 
Give those glasses to the bailiff.
…and those.
If I were being held as a hostage, I think being able to testify as a witness against my captors later on would be pretty low on my order of priorities.
Re: glasses:
“Put all the money in this brown paper bag, and make it snappy”
“wait a minute until I put on these goofy glasses.”
Ah yes, I had missed that the OP was referring to a hostage situation. My comment referred to a robbery situation, which is quite different.