how does my "neighbor" hear my private telephone conversations.

This is completely strange, and very long. I've exhausted all my ideas, and need fresh ones.

Some background.

1. my neighbor is old, very very old. Also, they are not very mobile. So something like creeping up to the window and listening in is out of the question. Although, a very long time ago (decades) they did used to hang out near an air condition vent, listening to our in person conversations.
2. when I say neighbor, I mean they live in a small house connected by a breezeway to my house. I do admit they are rather close. Yes I do have access to thier house.
3. i have no real idea of thier level of technological expertise. They are pretty manipulative so even though I'm under the impression they're very limited on expertise, it's possible they know more than they let on. Let's just say at this point, they say they have difficulties placing calls to thier saved contacts on thier jitterbug flip phone, but when your not looking they're already on the line with someone, like five seconds after you walked out the door. As far as we know they do not have access to the internet, but who knows. They do know how to navigate to at least a limited number of websites though. (Slight fear of them seeing this post, haha)
4. they digest far right media. This in itself doesnt seem relavent, but I suppose, in my head, this might be able to give them awareness of the types of technology that one might use to pull something like this off.
5. It is remotely possible that someone could have installed something inside the house maybe about 15-20 years ago, and given the neighbor access to it.
6. they are on a limited income, and are not independently wealthy. Any technology would have to be no only easy to use, but on the less expensive side as well.

So... Maybe about once a year for the past few years a topic or phrase that was talked about over the phone would come up in conversation the next day. Not a big deal, written off as coincidence. That's just how it goes sometimes. Well now, we've had a falling out. For the past few weeks they have brought up many private conversations I have had over my cell phone with at least 2 different people. They repeat not just what I say, but what the person on the other end of the phone says as well. I say, "Man, im pretty sure they're hearing my phone calls." The other person says, "Maybe there's a bug somewhere." The next day they start to prattle on about...a bug on the wall. But not a real bug...oh what do you call those things...you know, bugs that know things. Or I say "I'm worried about this escalating." The other person jokingly says "Oh, don't eat or drink anything from them, unless they take some first.. They may try to kill you." The next day neighbor is handing me a concoction they've made. "Oh, I've just sat down with this mixture I've created for my health. Everything I put in it is sitting on the counter there. (Cue various herbal supplements / tinctures) here have the first sip... it's not going to kill you." They are bringing up / creating situations centered around private converstaions from the night before. They may skip a day or two here and there, but it's a pretty regular occurrence.

Something worth mentioning, is that while im on the phone call, I will turn on my Bluetooth and use my earbuds. Everytime the buds connect, the call drops, and we have to call each other back. I figured I was pushing a button wrong or something and hanging up. But since the neighbor has gone somewhere, we have not been able to replicate the situation.

Things we have tried but have since been disproven:

• At first we thought we were leaving windows open and they could just hear it...but all windows were closed.
• maybe they can hear through the walls somehow, they are thin. But its never been a thing before. (why would they have to hang out by aforementioned vent, then) We blast the radio real loud and see how much we can hear from neighbors porch. Can't make out exact words and doesn't explain hearing the other person.
• well thier radio automatically connects to iPhones ( un-updated iphone from the air drop debacle/ f-ed up feature of the radio involving nfc and bluetooth) and it did pair with my phone at some point. Maybe they can the other person over thier radio. But we tried to make it work and just cant replicate it.
• we've checked obvious places for a walke talkie looking receiver. Nothing.
• we've used one of those cheap bug detectors off Amazon and checked the house...and the vent. No wires comming out of strange places as far as we can tell.

I'm at my wits end. What could they be using and how can I stop it? It maybe all a coincidence, but then its as much so as Facebook / Google targeted ads that arent listening your conversations. I mean, what, are they an advanced algorithm that can guess what your thinking based on all available data on you?

Help! And thank you for taking the time. Also, sorry about the format / spelling getting all this out on mobile is tough.

TL:DR. My really old neighbor seems to hear my both sides of cell calls to at least 2 different people. Is there simple, rather cheap technology put there that they could be using. And how do i go about finding it / making it stop.