Do you think the price of the 12 will go down on the day of the 13 release or would it be a few months later ?
It was never the case with Apple products such as Iphone. Let me explain:
1) If you live outside of the countries with official Apple stores, then you are dealing with wide sort of resellers(official and grey market). Under these conditions, older Iphones tend to have a price drop, which could motivate you to buy older one.
2) If you live in a country with Apple Store, then you will never get a discount on unlocked iphone through official means: Apple will just take them out of sale or decrease in hierarchy(iphone xr, iphone 11) and set $100 lower price tag. That is it in terms of the price drop. Well obviously there is a lot of sales going on with carriers which let you to buy at a significantly lower cost. But these deals are happening all year around and reach the peak close to new iphones. So when actually new phones are released, mostly carrier stocks are dried out, so you will not see price decrease. As a proof, you can skim through the websites of all carriers and can see that they are managing to sell iphone 8s at $349.