Should a negotiator use eye contacts much and why ?

It is important for the Negotiator to have good eye contact while dealing with any vendor or parties. Having a good and direct eye contact means -

1) You are acknowledging and giving importance to the person with whom you are discussing or negotiating.

2) You are attentive and not distracted during the negotiations

3) You are ready to listen and observe what the other person is saying

4) You respect the person and are giving importance to his presence and thoughts

5) You attach seriousness to the matter being discussed. 

If there is no eye contact, there is an element of casual attitude and lack of interest that you exhibit. 

Having good eye contact does not mean you STARE or LOOK at the other person with different eye expressions - That will make the person uncomfortable and may cause restricted communication. 

It is best to be calm and composed, look the person in the eye and use your voice modulation in a manner that takes the discussion further to a positive conclusion.