Not too often does a caller mention eye contact during sex specifically, but once in a while one will. Usually during oral sex is when they seem to enjoy it the most. Some might feel a bit uncomfortable with that prolonged eye contact during such a moment, hence why some prefer darkness. That level on intimacy can be a bit much for some people to handle. One man in particular said he loved it when a woman looked deep into his eyes when she had his dick in her mouth and he just adored it when she did. It would be a bit of an odd thing to ask for specifically though.
Gazing lovingly into the eyes of one you love while you’re being intimate with one another can be a wonderful thing if you’re both into it. If one partner is a bit shy or inexperienced, they might blush or feel overwhelmed by that and look away or just keep their eyes closed. It always seemed odd in movies if someone kisses with their eyes open, since your faces are so close together. That is one time eye contact is a bit weird. They’re so close, they’re distorted and blurry, especially if you normally wear glasses.
On the phone during phone sex, it’s often best if you don’t need to worry about that at all. You usually would be horrified if you could see some of the callers, though some send pics and look fairly normal, others are anything but. So mystery can go a long way and no worries of laughing or putting anyone off. Sometimes laughter can overcome us at an inappropriate moment and nothing would ruin a moment more than if you burst out laughing if you had eye contact and weren’t ready for it. Just ask if you’re unsure if they enjoy it.