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Ok, that was me going bonkers....
Just kidding... Your questions are great. I hope other folks reading this are gaining something: they're good questions.
I personally have never seen an Oncidium rebloom on an old spike. Which is not to say it could never happen, it's just to say that I personally have never experienced that. What I think you're probably seeing is the leftover green / clear tissue that suported the old blooms, and if you waited another week or two, you'd find the entire spike begining to die down from the top.
On all of our Oncidiums and the Intergenerics bred through them, when the blooms start to go, we just take a new razor blade and lop the spike off altogether so that the plant doesn't expend energy keeping a last little flower alive when it could be growing something new. That's what I'd recommend doing.
BUT: can you get close enough to the spike with a camera to post a pic? If I could see what you were talking about I'd be able to tell you more for sure. If it is actually reblooming from the old spike, that would be a novel thing (for me anyways... I may have been clueless all this time (!!!) Hope that helped some....