Thanks Randy. The front bumper tube that I bought on ebay is 2″ diameter, and the end caps match what you describe. The rear bumperettes I got from Karl are the same 2″ and the pairs of end caps are joined by a bridge that may originally have connected to the bolted end bracket. About the center of the parallel rear tubes there is also a clamp that was originally nickel plated, and it is held in place by a bolt through a small plate that says “Pierce Arrow.” I don’t see a maker’s name on any of the tubes, but there is a lot of rust and paint to remove, so there may be something there I’m not yet seeing.
As you say in re your bumperettes, there is probably no way of knowing if these came from a Series 81 like mine, or another model year. It is interesting that the Series 81 parts catalog shows no illustration or mention of any sort of rear bumper, either a single tube or a pair. I saw on this forum awhile back that George Teebay thinks there might originally have been no rear bumpers on the Series 81 and thus all such are aftermarket items, hence their not appearing in the catalog?