Well, Jim Becker is closest to correct.
I was tire, wheel, & rim buyer at FARMALL from 1979 to December 11, 1981. Electric Wheel in Quincy was owned by Firestone, they stamped ALL their rims & wheels Firestone. French & Hecht in downtown Davenport and their small Wheel plant in Walcott, Iowa was owned by Kelsey-Hayes that was owned by Fruehauf, and their rims were stamped F&H. Motor Wheel in Mendota, I'll was owned by Good-Year, their rims & Wheels stamped Good-Year.
The rear rims, double bevel during the 86&88 series were split between EWC and F&H 50-50 except for a couple specials which EWC got most of those, like the 20x30 rims, 21x32 & 27x32 which all had cast malleable iron mounting blocks RIVETED to the inside of the rims, and the 9x42 high clear 686 & H86 had a 12.4x42 tire option that EWC welded 8 triangular plates inside the rims for Farmall.
The 16x38 and 18x38 10 bolt duals for the 1586 and later the 5288 & 5488 were made by Titan Proform in Canada, they bought the rims from French & Hecht until they bought French and Hecht, and about that same time Titan bought EWC too.
The tires were split between approved suppliers based on percentages. FIRESTONE in Des Moines got 38%, Good Year got 37%, BFG got the remaining 25% of the bias tires and 100% of the radial rears. And Armstrong in Des Moines got 5% of the 5 highest usage tires, 10.00x16, 11.00x16, 18.4x38 6 ply, 18.4x38 8 ply, and 20.8x38 8 ply all R-1 rears.
I would imagine FARMALL and the other IH plants, like East Moline, Louisville, and the smaller plants like Canton, I'll, Memphis, split rim and tire sourcing in a similar manner, I used between 16 to 20 semi-truck loads of tires, rims, & wheels A DAY depending on the amount of duals ordered, and duals ordered with a tractor were available without tires, or with tires that had to match brand & ply with what was on the tractor. Plus FARMALL had Brand Preference, you could specify exactly the brand you wanted on your tractor, but only on the rears.