Redweek is a reputable advertising website.
They have two services: 1) do-it-yourself for about $50 in advertising costs, and 2) full-service with starts at $350+ a percentage, based on the how much it sells for.
The real question is: Does your timeshare have any resale value? -
most don't.
Generally, only the top timeshares deeded during high season have any resale value: Westin, Sheraton, Marriott, Hyatt, Hilton, Disney, and some Wyndham point ownerships.
I am not an expert on your timeshare, but I doubt that Villas at Southgate has any resale value.
In which case, you should consider giving it away - here is some info. about that:
How can I give my timeshare away on TUG:
http://www.tugbbs.com/forums/showthread.php?t=132509
*I just checked eBay and Villas at Southgate is selling for $1 on eBay, with free closing, and free 2016 maintenance fees, with no bids, so you should consider giving it away.