What is there to know, especially when he had driven manual transmissions and had downshifted on downgrades? Every automatic I've seen has a way to manually shift gears. Isn't this just common sense? Granted my current 6-speed automatic has more gears to select from than my previous which was 3 speeds plus overdrive, 2nd gear on that was a fairly low gear.
The minivan in question (mid-nineties Dodge Caravan or Grand Caravan) had an automatic with four forward speeds, as did the 1986 Nissan Maxima I used on the same grade. I am sure the brakes would have stayed nice and cool if he had coasted down in second gear, probably identified as 2 or L2 range on the column shifter (in the Maxima it was 2 range on a floor shifter). I blame a gap in instruction. As he explained it to me, downshifting an automatic to go down a hill is a skill, and he had neither been taught it in driver education nor picked it up elsewhere.
I think there may also be common misconceptions about how automatics work that prevent people from realizing they can be downshifted for hill descents just like manuals. Torque converters have a lot of slip at low engine RPM, so most people recognize the term
slushbox for an automatic. This may fool people into thinking slip is also high at high RPM, and thus that engine braking is not useful or available in a gear range that does not have lockup. In fact, neither is true. Slip goes down to about 5% at 2000 RPM. There is in fact a standard test for transmission function, the stall test, that relies on holding the wheels with the brakes and gradually hiking engine RPM until it stalls at a pre-determined RPM that is published in the vehicle's service specifications. If it does not stall, this is a sign the torque converter is permitting too much slip and needs to be replaced. When an automatic is downshifted to hold speed going down a hill, the crankshaft is usually turning at 3000 RPM or higher, so slip is basically negligible whether lockup is available in that particular gear or not (some transmissions are designed to have lockup all the way down to first gear).
One peculiarity of transmission design for some makers, such as Toyota, is the use of one-way overrun clutches to prevent engine braking when the car is coasting. Effectively the car is in neutral since the clutch prevents the wheels from applying torque to the engine crankshaft. I suspect this is an emissions control/fuel efficiency measure since it allows the engine to drop straight to an idle when the driver is not demanding power, but it does mean that if the driver wishes to elicit engine braking for a hill descent, he or she has to choose one of the L ranges so that the one-way clutch is bypassed.