I was under the impression that ebay had a "going going gone" period at the end of each auction, so that if there was a flurry of activity at the end, it would extend the end time of the auction until everyone finished getting all of their bids in.

Nope, eBay has always ended at the exact second set when the auction was created. UBid does do what you describe, complete with a flashing "going going gone" graphic.