I also have identical twins - boys . One of them was born with congenital ptosis, and the other was not. This has caused some confusion in our extended family, as well as with outsiders, as to whether or not they are truly 'identical'. I have since found a great deal of information supporting the fact that this can happen, even with identical twins. We also have an appointment with a specialist who will be performing the corrective surgery. My father in law had this procedure performed as a child as well, and his surgery went very well. It is a simple procedure, usually done on an outpatient/day surgery basis, although with children, general anesthesia is used (as opposed to local as with adults), so their reaction to the anesthesia will be a factor as to whether they are released immediately after surgery or kept under observation for a period. They simply cut a tendon in the eyelid, shorten it slightly, then re-attach. The entire process shouldn't take more than a few hours, including recovery and observation. A bandage/patch is rarely used in pediatric patients, but they will prescribe antibacterial eye drops. As far as after care, just follow normal wound care - keep the area clean and dry. This is what I have been told, anyway. I will update after the procedure.
I did read some of the other responses, and while I would normally agree that having a surgery like this for 'cosmetic' reasons is not warranted, It is a slightly different issue when you are talking about identical twins. Part of their identity, like it or not, as they grow up is going to be in the fact that they look alike. Having an identical twin brother seems to make the drooping eyelid seem that much more pronounced, and causes well meaning people to ask questions such as "What happened to his eye?", as well as causing my own family members to state that you can tell them apart because " T. is the one with the lazy/droopy eye." I know that there will be enough rivalry/competition with each other over the years because of their being twins, but I do not wish to add the stigma to little T. of being the "different" looking twin. I truly believe that if they were singletons, people probably would not notice the ptosis nearly as much as they do with there is an ALMOST (but not quite) mirror image standing next to him. Unless you have twins yourself, you couldn't really understand this.