Yes! I had exactly the same experience. Quitting habits like smoking, drinking coffee, or playing video games has always been much easier during those periods, and it felt like it happened on its own. It was mind-blowing to notice that after it happened a couple of times.
Yes, I know it's not that hard, but lately I've been going through a period of low mood, and I really cannot stomach the idea of diving deeper into the Abyss for a couple weeks while my receptors downregulate. It's hard enough already as it is.
I had some success systematically reducing it over time rather than cold turkey. YMMV. It may feel silly measuring out coffee and reducing it by just a small bit every day but it's worth it to avoid the fully withdrawal symptoms.
You just explained your cycle though. At least you can see it, up to you on how to get out of it. It sounds cliche but it's entirely in your power to change it.
The reason you can't is because in this sentence, you are saying you can't (or won't).