TL;DR: Why did Quirrell have to maintain eye contact with Harry when he tried to jinx Harry during the Quiddtch match? Are there other spells, jinxes, or curses that require eye contact?
In Philosopher's Stone, Harry, Ron, and Hermione believe that Professor Snape was jinxing Harry's broom during the Gryffindor/Slytherin Quidditch match:
The afternoon’s events certainly seemed to have changed [Hermione's] mind about Snape.
‘I know a jinx when I see one, Hagrid, I’ve read all about them! You’ve got to keep eye contact, and Snape wasn’t blinking at all, I saw him!’
Philosopher's Stone - page 131 - Bloomsbury - chapter eleven, Quidditch
It is actually Professor Quirrell who jinxed Harry's broom during the Quidditch match; Quirrell says he would have succeeded at harming or killing Harry if Hermione hadn't set fire to Snape's robes, causing Quirrell to lose eye contact with Harry
‘But Snape tried to kill me!’
‘No, no, no. I tried to kill you. Your friend Miss Granger accidentally knocked me over as she rushed to set fire to Snape at that Quidditch match. She broke my eye contact with you. Another few seconds and I’d have got you off that broom. I’d have managed it before then if Snape hadn’t been muttering a countercurse, trying to save you.’
Philosopher's Stone - page 209 - Bloomsbury - chapter seventeen, The Man With Two Faces - Harry Potter and Professor Quirrell
Q: Why did Quirrell have to maintain eye contact with Harry when he tried to jinx Harry during the Quiddtch match? Are there other spells, jinxes, or curses that require eye contact?