Well . . .
If you are old enough for the name Betty Furness to ring a bell, you'll recall that Westinghouse was a big player in the American home appliance market back in the day. So far back that probably a rock in an ancient cave somewhere has the brand name hammered into it. Nonetheless, I think Westinghouse came to be best associated with its front-loading washing machines though it made just about everything else too.
My history is not great but I'm sure someone will kindly fill us in as to where I'm all wet -- so . . .
During the 1950s Electrolux and Hoover reigned but big across the board appliance makers like GE, Westinghouse, Hamilton Beach, etc., took up the slack with their own offerings. The T-4 you have is ingrained in the memory of many due to it or a similar model being used in an "I Love Lucy" episode. The company however also produced upright vacuums and a long popular hand vac predominantly made of Bakelite plastic. They later went on to produce or source an upright that was similar to a low-profile model Singer was making. As Westinghouse vacuum manufacture continued, canister vacs came more into play during the 1960s and into the seventies I believe.
I have actually owned one these so I'm pretty sure there's a Model T-3 as well the difference being mostly the paint job. If you feel you've a real interest in vacuum collecting and restoration, this a model that will certainly help show you what it's all about.
Mine came near complete save for the suction wands which are specific to this model. Every now and this model comes down the pike with various parts intact you either pass or buy what you can use. Unfortunately, I wasn't able to invest much time or funds in making mine complete.
At this point in time, even if in shape to run, I wouldn't recommend it as a spare machine and it seems a shame to make a lamp of it but its your call. There a lots of old vacs that I thought to be rare, Rexair for one, but have found that others are much harder to come by.
As a commodity, though the interest is limited, if you clean the machine up (safely removing dirt and grime without promoting rust, shining up metal outer components) then carefully keeping an eye out for match-up of tools that would have been originally supplied with this model, it might ONE DAY prove worth auctioning off if you don't want to keep it.
If you do opt to auction, start with a reasonable reserve that you feel would compensate your effort invested up to the point of sale. In other words, you'd be making plain that the machine wouldn't be released without a specific minimum bid. That said, things can go either way.
Hope some of that helps. If I can find out anymore as to history. I'll leave it here. There's a link below to Charlies website that may prove helpful as to your T-4 and even more elpful are his other pages there if you're serious about collecting.
http://www.1377731.com/museum/westhous.htm