I think it's usually through watch dealers or a jeweller. You may try to visit a Patek AD and ask whether they can help to sell the watch.
Watches
A community for watch & horology discussion.
A respectable forum like watchesuseek or rolexforums. there are respectable sellers selling pateks on both as we speak.
The only issue is, you won't have a reputation on there so buyers may be wary. But go on there, engage. Be as transparent a possible with the papers, authenticity, receipts etc, and you should be good. It's a nice direct way to sell it with no middle man cut. So you'll need to price accordingly with that in mind.
Auction house like sothebys or Hindmans, a bigger watch reseller, or reach out to local Redbar group and see if any private buyers are interested
Easiest and most money are 2 separate things... Your best bet is to find a trusted dealer or Auction house.
Don't waste time on a forum or eBay or such for a one time sale of a high value item. Too many problems could arise.