The non elect believe in their heart and proclaim with their mouth that Jesus Christ is Lord? That’s not possible I don’t think.
Certainly you admit people can confess that Jesus is Lord and still be non-elect. so if you are going to make suppositions about someone's heart contrary to what they say this certainly doesn't 'prove' anything as you initially stated works prove faith.
BTW, were you raised Calvinist? I was. Most Calvinists who fight for it converted to it. Doesn't prove anything but I find it very interesting.