I tend to decide before I first walk in to do the deal what I want my changeover $ figure to be and that is my negotiating point to start from. Always do my homework around what my trade is worth privately too.
If I'm miles off and know I'm pushing sh!t uphill with a fork, then I just resign myself to the fact I'm going to have to sell privately and be patient.
I've been through this twice in the last 9 months and had to go through one each way, so to speak. And yes dealers are burglars so you have to be battle ready.
A lot of it comes down to so many variables like how much they need to move a car, day of the month etc.
The private sale of my last car followed by purchase of my 328i was worth an extra $20k made up of $12k extra on the private sale versus trade in offer and approx $6k better negotiating on new without a trade so it was a massive difference. As a side note at one BMW dealership they offered me base red book value on my trade so I did the same to him on the demo 328i. He didn't know what to do. I explained that red book obviously works in both directions and it's not a tool for the dealers benefit solely.
On my wife's car I traded a Pajero on a Land Rover Defender and the difference was only worth about $5k and the Pajero was a dog, no log book and service history etc and was a rushed job when I bought it second hand due to circumstances at the time and most definitely my worst purchase in my car history. So I was glad to be able to dump it at the dealer and not have to think about it and very much to my surprise the Land Rover dealer hit the the changeover $ after much back and forth nonsense that you go through. I couldn't saw them over quick enough. Interestingly when I spoke to the dealer a couple of weeks later because I'd forgotten to get my toll road tag out of it, he said that the wholesaler had decided they didn't want the pajero after they'd seen it and were stuck with having to take a massive hit on it. Hilarious. Was so nice to win one against them.
Anyway hope that helps any of you going forward.