2003 Ex 6.0L limited 2WD 120k miles.

Hello,

I have a question concerning my alternator. I replaced my alternator about a year and a half ago. Then in the last 2 months I noticed when parked with the engine running, I would get a clicking noise like every 30 seconds. (I now believe that to be the alternator engaging and disengaging). About two weeks ago, I began to experience the battery light coming on in the dash while driving. Then it went to flickering on and off. Now its back on steady. I went to advance auto and my batteries were under warranty. Guy checked batts and said they were good, but then I said wait, lets unhook them from each other...then they turned up bad on his gauge. I had him check alternator at the same time unfortunately while the batteries were still connected and he said alternator was fine. So with new batteries I still get battery light coming on steady. So I had one of those cigarette lighter charging indicator devices and plug it in and it shows 12.05 volts with a red light on (system isn't charging). I checked terminals, cleaned terminals/posts everything ...still not charging.....then I went to the alternator while trunk running and pushed down on the charging post on rear passenger side of alternator. Suddenly I hear the click like the alternator engaged and the meter in the cigarette lighter shows 13.20-13.50. It stayed on for a while then after 10 min. it clicked off again. So I went back and pushed down on the alt. charging post connection again.....and wah la click, engagement and its charging again.

My question is: Is it normal that the alternator engages and disengages while parked with the engine in idle? What I heard in the beginning? Or should alternator stay on continuously with out that clicking? Next.... I read that the voltage regulator is an integral part of the alternator itself and the whole unit must be changed (its a Tough One alternator bought at Advance with a limited lifetime warranty...if connector is bad does that mean alternator is bad or is it maybe my wires and not the alternator)... I don't even know how I would claim the warranty. Is there a part number for the connector? Its the charging post connector that I'm pushing down on and not the voltage regulator black plug. The charging post connector has a grey rubber housing sleeve. I tried pulling on it to unplug it and it wouldn't budge..I didn't want to break it off....should it just pull off or do I have to squeeze and release or some other trick?
I noticed while I had my finger down on it in the charging mode..the connector got hot real quick (when it was charging) when it wasn't charging it was cool to the touch. So much heat might have melted or degraded the connection point on the alt charging post itself or the internal part of the wire side connector? Any advice? Should I just buy a new alt or is there a way to test the wire side of the charging post connector? I hope this helps some of you out there.....press down on the connector and see if your system starts charging..mine did. BTW...two months before this I have been getting at times a no start when trying to crank up. Batteries seemed fine (lights and all worked) but absolutely no electrical to the starter (glow plugs came on, but go to crank and nothing). Also the clue to my batteries being weak was that the truck started to have slow start conditions when it would start.... it would engage starter but take a while to crank over. I'd shut off all electrical (AC, radio etc) to crank it up and noticed this helped a bit.