My car thinks the key is always in the ignition

It wouldn't bother me much, but it does not allow the remotes to work. Occasionally, like 1 of every 10 times, when I remove the key after driving, the lock and key works as designed and the remote works (no beeping when I open the driver's door). So I thought, maybe something was getting stuck in the lock.

I read here: https://www.mazdaforum.com/forum/mazda3-26/key-sensor-problem-12858
That there was a piece of metal that the key moves out of the way to tell the car if it inserted or not. Yesterday I took apart the Ignition Key Cylinder (just like this: https://www.autozone.com/interior/ig...539_0_0_141469 but without the long thin metal hook, don't know why . I gave it a good clean as the keys were starting to stick a bit. I removed and reassembled the pin tumblers (8 of them), also strung out a bit the springs to make them a bit perkier. Now it works like new, but I did not see anything that the key pushes out of the way, besides the little pin tumblers. The car still acts as if the key is always inserted (beeping and the remote is not responding).

I don't know how to fix the issue. The only wires getting to the ignition lock cylinder, are getting to that black attachment (in the AutoZone link above), which I am guessing is the FOB key transponder. May it be that, that black part is to blame? I wonder if that has some sort of metal detector in it. I figure it cannot be the transponder itself, since the car can sense when a "dumb" key is inserted. Maybe I missed something. There were a couple of plastic parts that moved and I could not figure out what they did. Again, replace a $500.00 part for a tiny piece of plastic sounds sad (particularly for my pocket). I wonder if somebody who knows could help me here. What senses the key in the ignition? Thanks in advance.