There are two important factors to concider when starting your auction to get maximum profits. The first is for how long should the auction run for? And the second is at what time should the auction start/end?
You have five options for the length of the auction, 1 day, 3 days, 5 days, 7 days and 10 days. You need to concider the day the auction is going to end., this is for posting your item, so ending the auction on a week day is a good idea. This attracts buyers wanting next day delivery, or to receive the item within a few days. An auction ending Saturday afternoon will mean the buyer will receive the item Tuesday at the earliest. This may not be the best time to end the auction.
A 7 day auction may be the best option as it covers all the days of the week. (including peak days like Friday night and Saturday) It is not too long for buyers wanting the auction to end so they can get the item. 10 Day auctions may be too long for some buyers to wait and they may loose interest. Hovever, 10 day auctions do allow time for more people to see the item you are selling.
The worst time for an auction to end is between 10PM and 7AM, this is because buyers will be asleep, not on eBay to bid. The best time to end an auction is probably between 8PM and 9PM as people will be at home, and probably not asleep. They will not mind going onto eBay at these times.
To summarise I think the best day to start the auction would be a Sunday at 9PM for 7 days, or Thursday at 9PM for 10 days.