There is a lot of information on the Forum about the windshield washer pump and system. I hit the Search button above and did a search on windshield washer and got a lot of hits. This one shows what the '58-'59 and the 60 look like. There are are two different models. I think the bottom one is for the '60, which mounted off the generator. The windshield washer control on that dog leg in the picture is a vacuum operated switch, and according to some, is known to have loss of vacuum problems.
As for these chrome packages, it is hard to say what their quality is. Some have had problems with valve covers leaking after they have been chromed. The OEM valve covers for your '60 Tbird were yellow with the FORD name on them. I have chromed ones with the THUNDERBIRD name on them, which is not original for that car, but I like them. Chroming can be a problem with pot metal on our cars. The hood air scoop, those curved pieces around the tail lights, and perhaps other parts, are known to bend on you due to the heating process during chroming. I did not use my originals to be chromed. I bought extra parts and chromed them. I had bending problems with my air scoop and my curved pieces around the tail lights with one of them. I was able to get it in place. The air scoop was another story. I had to buy another one to get it right.
The engine picture is of an award winning fully originally restored '60 Tbird.