The best days to sell gift cards on eBay are those when people start shopping for major holidays. This includes Thanksgiving weekend, the week before Christmas, the week before Mother's Day and Father's Day. "Black Friday", the Friday after Thanksgiving, is the best sales day of all of these ideal dates.
Sundays! If you can time an auction to end on a Sunday afternoon, you have the best chance of reaching the most number of people. If an auction has to end midweek, try to have it end early evening. Avoid auctions that end in the middle of the night or on a Saturday or Sunday morning.
I think that the best day for selling gift cards on ebay would be on Sundays. I think quite a bit of people are free on Sundays as that is a religious holiday and that would bring more people to buy gift cards on ebay.
My opinion is that the best time of year when gifts are sold very well is the period around Easter and Christmas, because in this period that all dedicate many shops selling souvenirs should have full stock not to be taken by this time of year is very generous people and they purchased many items.