If you officially had 65, early 66, 4 piston calipers, the dust boot is retained by the use of those "rings"
You can tell if you have later calipers, if there are two grooves in the bore of the caliper.
One groove to seal the piston, and the top groove for the dust seal.
Early calipers have one groove in the bore, for the piston seal, and the dust boot "ring" is on the top of the bore.
The dust boot seal goes around the ring, holding it in place.
Dust boots are somewhat different between the 65-66 ones, and 67-72 ones.
67-72 ones can be used on 65-66 calipers by cutting off the lip of the boot, where it would be in the groove of the caliper.
But official 65-66 boots won't work the other way around on 67, 72 calipers.
Possible you have mix matched caliper halves from different year calipers.
After taking a closer look at the pictures of your caliper(s) you have the "early" style, design.
Nothing wrong with that, as they all work.
If your running into problems with the dust boot seals, you can get "kits" from any Mustang restoration, vendor, of your choice on the internet.
But they have to be 65-66 kits.
Mustang, and Mopar, Kelsey Hayes calipers are basically the same things, except how they attach the brake flex hose to the caliper.