Any halfway decent local bike shop will have what you are missing, which appears to be a cable and a boot. My experience with those bikes is that the V brake calipers they came with were quite crappy, and benefitted from replacing the cable and housing with better stuff, I remember that "schwinn" used crappy unlined housing and galvanized cables. YOU CAN"T REPLACE THE BRAKE CALIPER WITH THE ONE UNCLE JEFF IS SELLING, the arms will not be anywhere close to long enough to clear those big old tires, most standard V brakes measure around 100mm from bolt to cable anchor, OCC brakes are more like 150mm if memory serves.
The tricky bit of all of this being running the new housing through the frame, which I do in this order:
1. run the new cable through the old housing back to front.
2. pull the old housing off, leaving just the new cable in the frame routing.
3. carefully slide the new housing over the new cable front to back, taking care when you get near the entrance and exit, manipulating the cable as needed while avoiding putting a kink in it.
4. once routed, pull the cable out, trim housing as needed, install housing ends (ferrules) and hook the brake up.
5. at this point, you'll probably have to true the wheel, fiddle with the brake a bunch, ramp up the tension until you get a decent feel from the lever, and you'll still have a brake that only works OK.
Hope that helps, feel free to ask me questions, I'm just a grouchy professional bike mechanic with a soft spot for Schwinns and cool old bikes, since it's what I grew up on. I actually sweet talked my local toys-r-us into selling me one of those OCC choppers a week before they were released, then had fun week riding around on what is objectively a pretty poorly made bike.