What DeniseM says is true in almost all cases. There are some exceptions, notably Hilton or Marriott premier weeks, but that is going to be the rare situation.
Your best bet is to look at completed eBay sales for your exact timeshare. I think you might be surprised how low those sold prices are going to be. With some timeshares, the value is not only free but some require the seller to pay for closing and maybe even adding an additional perk, such as use of a free week or a gift card. Without knowing exactly what you own I would say that $1200 may not realistic. You could also search the giveaway forum here on TUG to see if your timeshare is listed and if so what prices.
Giving it away or “selling” it is easier than you may believe. Find a taker and have LT Transfers (just one recommended closing company on TUG) handle all the paperwork for a nominal fee.
Finally, you may see some timeshares listed on certain websites for thousands of dollars. These are unrealistic prices and these timeshares never sell.
Good luck!