Shutting your eyes and then looking at the sun should protect your eyes from damage from the harmful UV rays that can damage your eyes when looking at the time.
Still I found it too intense to look at the sun for more than a minute even with my eyes closed so the suns UV rays can still get through the eyelids.
But closing your eyes does help protect your eyes some from the damaging effects of the powerful suns UV rays.
If you want to look directly at the sun you should put on a welding helmet and then look at the sun through the welding helmet Lens.
The welding helmet lens protects your eyes from UV rays from welding and will also protect your eyes from the suns UV rays.
I've done that and by wearing the welding helmet I was able to stare at the sun without any eye damage.