My approach was always to be disinterested. As if I'm not even shopping for a car that day. I tell the wife to go to the mall when I'm in this stage of the process. She's way too easy to read. I got screwed sideways on a Lexus about 12 years ago because they could read it all over the wife's face. She was either getting that car or I was living out of a backpack.
At any rate, I play it nonchalant - make me a ridiculous deal and I'm all checkbook. Otherwise, I got a ball game to watch at noon.
Got an awesome deal on my most recent F150 purchase, doing just that. The key was, I actually could take it or leave it. Plenty more out there where this one came from and there was no urgency to my buying now, vs 3 months from now. The salesman felt a lot more urgency than I did.
Your point is right, there's not a TON of room to bargain on an F150, but what I do know, is that I left nothing on the table.
I walked in to multiple dealerships, test-drove at least a dozen trucks, told them all I what I was doing, and told them exactly what I was looking for-- specifically, I needed a truck that would tow at least 11,000 lbs with all of the appropriate towing options and gear ratios to do so comfortably-- and let them call me over the next week to throw their best at me.
Worked like a charm, and I even lucked into a Platinum package instead of the Lariat or King Ranch, because it was the only one the dealer had that included all my towing specs. That salesman was motivated.
And yes, my i s c & a aggie wife stayed out of it. Similar to BC, she got me completely hosed when we bought her Toyota Solara convertible years ago.