If there is partial vision it is essential NOT to wear a patch 24/7. If you decide to wear a patch it should be no more than half the waking day. If you wear a patch 24/7 there is a chance of complete loss of sight. This a question best asked of an opthamologist. Often, stroke damage affects the cranial nerves and the eye becomes "frozen" in position. A patch worn for several hours a day (when walking) will help a person retain balance.
I wouldn't try to have him wear an eyepatch if his doctor doesn't recommend it. There is the possibility that he needs to re-train his eye muscles and a patch would make it harder to do. If you are curious as to whether that will help, either ask his doctor yourself, or have him ask his doctor. Regarding the blood clot that caused the stroke, was it removed surgically? If not, probably the doctors involved have discussed what to do to remove it or move it along and have him on Coumadin or another blood thinner? Does your dad know what he was prescribed and why? If not, someone else from the family should call and go over it with the doctors.