This is something we do alot of in most Tai Chi systems, I was watching a program where a doctor recommended standing on a single leg with the eyes closed as a weight bearing exercise to prevent bone loss of osteoporosis. Under 30 years of age 30 secs standing, over 30, I missed what they said but I think it was a shorter time.
we use these progressive exercises to retrain balance, coordination and control, (propreoception) in sports rehabilitation, but I advocate one eye closed not both, there are also other things you can do to make it progressive, ie holding on with 2 hands if you cant balance, then one hand then one finger, then opposite leg moving forwards backwards, then sideways, then arms folded over chest the list goes on and on......... useful if you have had lower limb injury.
start with 10 second hold on each leg or swap if you fail or lose balance, gradually increase until you reach 30 sec on each leg, there is little benefit progressing past 30 seconds as additional benefits are minimal, when you get to 30 seconds have a ball thrown for you to catch either side or above your head.
regards
Gaz
I see this also used in Janda's method of muscle imbalance and correction.