Chris,
For what it's worth...these swaybar parts can sometimes be hard to find, so there are a couple things that might help you in your search.
The swaybar mounting plates (item #5486) in the drawing are specific to 1980-1986, and they are quite hard to find....mainly because they're quite difficult to remove, at least from a rusty truck or a junkyard truck. in 1987 the mounts became integrated with the cast iron spring seat. The 7/8" swaybars were all the same, so you can use one (and the mounts) from a later truck...up to at least 1994...maybe later.
Lots of people have gone to the junkyard and pulled both swaybars from a 90's truck and they swap right into a Bullnose.
I bought both front and rear factory swaybars for my 1984 Flareside, but I have so far only installed the rear, and I must say it made a significant improvement all by itself.
The rear bars are also all the same, so you can grab one of those out of a 1990's truck as well...but you'd have to modify/adapt the 8.8 axle tube brackets to mount on to the 9" rear diff (which I assume your 1982 has).
1994 F150 4x2 Flareside. 5.0 w/MAF, 4R70W, stock.
1984 F150 4X2 Flareside. Mild 302 w/ 5spd. Sold.
1980 F150 4X4 Flareside. 300i6 w/ 5spd. Sold in 2021.
1980 F100 4X2 Flareside. 351w/2bbl w/NP435. Sold in 1995