Steve,
I'm not fully versed yet on the electrical interfaces involving your description of the brake light and rear ABS light coming on after approximately 5 minutes of driving, but I can address why your rear brakes may, in fact, be non-functional, and offer a simple troubleshooting solution to find out.
I recently overhauled the rear drum brakes on my 92 2.3L Ranger, and installed a new wheel cylinder on the right side. During the attempt to bleed the brakes, I discovered that neither rear bleeder valve would pass any fluid. After some study in the the brakes section of the forum, I determined that this was likely caused by a clogged "due to age, and probably never been flushed" ABS Hydraulic Valve. This valve is attached to the inside of the frame just below the driver's left heel, and is fairly easy to access and R&R. Troubleshooting involves taking one hose off (the rear first, and see if you get fluid out of the valve, if not take the front hose off and see if you get fluid. If no to the first, and yes to the second, it's likely clogged. Your main problem is going to be getting the input and output brake lines loose from the valve without rounding off the nut heads, at least that was my problem.
Clogging of this valve due to rust or corrosion over time appears to be fairly well-documented occurrence. So, there's like a number of older Rangers running around out there with inop rear brakes.
Replacement cost is around $120.00 for the unit, cheapest I found was at Auto Zone. There are some forum threads which support bypassing this valve, due to its cost, and living without ABS.
Hopes this gives you a place to start.
Happy Holidays,
Ron