It has always been this way for me since 1988, when I bought my first car.
I've learned over the years, most times the real pushy - almost like their reciting from a script verbatim, have less than 2 years on the job, or in sales of any kind.
The one thing I have learned to receive everytime I'm met with what kind of rate/monthly/term, is I simply need your best price possible, the rest will naturally fall in place.
You have to do lots of pricing research ahead of time as well as pre-approval from your bank or credit union for a predetermined amount/rate and term.
There's quite a few online "cash for your used car" I've used to gauge real trade value. These sites will usually price you a bit lite, but from further research you still can gauge whethsr you may be able to negotiate more for your trade.
All thatasidet it is up to the individual to protect their wallet, and usually REQUIRES divulging the LEAST amount of information necessary to the salesperson.
Repeated responses of I'm looking for the best price, and if your store provides me with the best price, I will buy today. They need nothing else from you, if they want to sell a unit. Once you do have your price, it's at this time if you haven't already done so during negotiating price, have the pinstripes, wheel locks, any dealership advertisements, etc. as a condition of sale on the buyer's order
I'm not saying my way is best, but it has saved me a great deal of time. If I get the four square within 10 minutes of being on the lot, wanting to talk price (presumably to them as a cash buyer), I'm out the door, with a smile on my face, because I know I just saved a shit ton of my time and money.
Once price is agreed upon, I mention letting them have an opportunity to price my current vehicle. Then the game restarts, EXCEPT price is already locked down from a written buyer's order.
So you either negotiate into a price for your trade, or walk if they won't come up on the offer. They won't offer you what they are really ready to pay you for your car, at first, but stick it out, and you probably can get close to where you'd like, or walk.
Then repeat for the finance office, if you want to give them a chance to earn your financing. You will already know what you have, presumably from your bank and it's solid.
First thing I tell the F&I person after the initial introduction, is to let them know straight up front, I have zero interest in discussing extended warranty, undercoating, service for life, etc. they may suddenly forget or remember something else that is sooooo fantastic they just would not be doing their job if they didn't mention it to you. Be prepared AS SOON AS you hear that line come out of their mouth, to get up politely, and tell them that it is unfortunate we could not close this deal, have a good day.
Likely they will apologise, and the rest will go swimmingly, but be sure to check the numbers every step of the way, with your own calculator.