I can find only brief mentions in the two novels that followed Friday and Job, The Cat Who Walks Through Walls pub. 1985 and To Sail Beyond the Sunset pub 1987. (There is no mention of Shipstones in Job).
For completeness I've listed these below, but they are throwaway mentions that add nothing to the description in Friday. I would guess Heinlein felt he had sufficiently established Shipstones as part of his universe so they needed no further description in subsequent novels.
The closest we get in Friday is:
In studying the Shipstone corporate complex I did not attempt to study Shipstones. The way — the only way — to study Shipstones would be to go back to school, get a Ph.D. in physics, — add on some intense postdoctoral study in both solid state and plasma, get a job with one of the Shipstone companies and so impress them with your loyalty and your brilliance that you are at long last part of the inner circle controlling fabrication and quality.
So they involve plasma physics as well as solid state physics.
The Cat Who Walks Through Walls
Chapter 15:
No magic is involved. An electric catapult is a motor generator. Never mind that it doesn't look like one. In its acceleration phase it is a motor; electric power is converted into kinetic energy. In its decelerating phase it is a generator; the kinetic energy extracted from the capsule is pulled out as electric power and stored in a Shipstone. Then the same energy is taken from the Shipstone to hurt the capsule back to Kong.
Not quite. There are hysteresis losses and other inefficiencies. Entropy always increases; the second law of thermodynamics can't be snubbed. What it most resembles is regenerative braking. There was a time, years ago, when surface cars were slowed and stopped by friction, rudely applied. Then a bright lad realized that a turning wheel could be stopped by treating it as a generator and making it pay for the privilege of being stopped-the angular momentum could be extracted and stored in a "storage battery" (an early predecessor of Shipstones).
Chapter 27:
Starting about 2150 or a little earlier (I saw my first one the year I signed up) supreme swank for an Iowa fanner was to own and drive a working replica of a twentieth-century "automobile" personal transport vehicle. Of course not a vehicle moved by means of internal explosions of a derivative of rock oil: Even the People's Republic of South Africa had laws against placing poisons in the air. But with its Shipstone concealed and a sound tape to supply the noise of a soi-disant "1C' engine, the difference between a working replica and a real "automobile" was not readily apparent.
To Sail Beyond The Sunset
Chapter 20:
"I'm not sure. We were all the way to Olathe before we found a filling-station that also serviced Shipstones. While Hank was trading his stone for a fully charged one, I opened Polly's cage to change her sandbox - she had made a mess and the dragonwagon was stinking."
Chapter 21
"As a starter, try multiplying a thousand miles by two hundred yards, to get square yards, then call it horsepower. Use a ten per cent efficiency factor. Save the surplus power in Shipstones when the Sun is high and bright; use that surplus to keep the roads rolling when the Sun doesn't shine." (I could be glib about it; I had done the arithmetic many times in thirty-four years.)