As with anything dealing with time stoppages, the important question is what are the boundary conditions? In this case there is another question: Does the time stop propagate at the speed of light or not?
For example: I look at a start 8 light years distant. When did time stop on that star? Did it stop when I received the light (in which case eight years ago) or will it stop immediately upon me looking at it? If it's the former case then the motion of celestial bodies is very rapidly going to get messed up, if it's the latter then you can send messages back in time by morse code blinking.
Either way: all of these points are rendered somewhat moot by the fact that everyone would very quickly die. If you're not looking at yourself, time stops. You cant move anything. Solitary people are trapped, forever causing time to flow in their field of vision but unable to do anything about it. People in groups fare a little better, as they can keep time going for each other, but they'll have to sort out blinking and sleeping pretty fast or they're all going to freeze too. Even if a person remains in-time the air they're trying to breathe wont be without assistance
But lets ignore that technicality via the power of handwavium. Everything mentioned in this question still applies. How you deal with the boundary between time and not time is of utmost importance if you don't want peoples eyeballs being ripped out of their sockets by tidal stress, gravity failing to work or all creatures with eyes accidentally causing nuclear fusion with their peripheral vision.
Ignoring the purely physical though, lets assume comic book logic. The presence of living beings would be paramount to life continuing. Depending on your definition of 'eyes' and 'vision', our greatest allies here are actually mites and insects. They're ubiquitous in most day to day activities, number in the trillions and look everywhere fairly indiscriminately. Some insects (ants, bees etc) rely on polarised sunlight for navigational purposes, so the sun isn't going to suddenly stop (again, boundary conditions could lead to some hilarity if it did).
I'm assuming that in our comic book logic an 'object' caught in someone's LOS has time, so basically anything that can be seen by an insect, dust mite, tardigrade or Eagle will continue to function. This basically covers... well, almost everything. Automated systems in cleanrooms might have some issues, but you could lock a cockroach in a box and point it in the right direction to fix that.
TL:DR Not much change if you use comic book logic, everybody dies if you don't, watch out for paradoxes caused by the speed of light.