I noticed some of the early Thunderbird parts catalogs had both front and rear sway bars available.  Did the 1956 Thunderbird come standard with front and rear sway bars?  I don't think the bird I acquired has them.  All I have on the front is the stabilizer bar.

They only came with the front. I have an aftermarket front and it handles better. Never wanted a rear but from what I understand they help a lot if you want to go around a corner fast. Radial tires are also a great improvement in handling.