Thanks for the reply, I finally got a good possibility,
anyway, I do definitely agree that the problem is still around the ignition switch area. I was the one who went to purchase the ignition actuator and when I bought it, I took the old broken one to auto parts store to compare and for what I saw they were both 100% identical, I think the only difference is that the new one is shinier than the broken one, so, I really don't think that I need to replace the ignition switch from the other supplier, so by steps the things that I should do like you mentioned is first remove the ignition switch. (you mean cylinder right?) then check if the plastic rod (is it the one that goes in the actuator?) makes contact with the chime contact, is that correct? Also, is all this easily visible?
Also, if I remove the key cylinder will the chime still be dinging? Because if it stops dinging, I think this is a good way to determine if my alarm behaves this way thanks to this issue.