I looked more into this and found a more likely explanation.
At a high level, the hybrid system is composed of three parts - the gas engine, Motor Generator 1 ("MG1") which is used primarily to start the engine and to generate electrical power, and Motor Generator 2 ("MG2") which is mechanically linked to the front wheels and used to either propel the vehicle or for regenerative braking. All three components are connected to a planetary gear set (MG1 to the sun gear, the engine to the planetary carrier and MG2 to the ring gear.
When the vehicle is in regeneration mode with the engine off, MG2 will be turning with the wheels and, depending on the gear ratio between the ring and sun gears, MG1 will be turning at a factor typically greater than two times the rotation of MG2. This means that if the vehicle picks up speed while descending a hill, the RPM of MG2 will increase and the RPM of MG1 will increase by an even larger amount. Therefore, if the engine remains off, MG1 could eventually reach RPM levels beyond it design specifications which could cause damage.
However, if the engine is running during regeneration, the engine will turn the planetary carrier, which will reduce the factor by which which MG1 will rotate, thereby keeping MG1's RPMs within an acceptable range. I think the constant cycling of the engine that you are experiencing is the vehicle alternating between turning the engine on to manage MG1's RPMs and turning the engine off since the battery is sufficiently charged and the engine is not needed for regeneration.
This does not happen while descending the hill, it only happens
after I reach the bottom and I'm sitting at a stop light, in which case, at idle there would be no RPM's to manage?
I have another theory: heat management. Using and charging the electric drive system generates heat, including regenerative braking. When a heat threshold is passed, the electric drive system quits, even though there is sufficient charge in the drive battery. I have observed that if I have been driving the vehicle for an extended period of time going in and out of electric mode frequently, then as soon as my foot releases the brake pedal from a standstill the gas engine will turn on
even when there is sufficient battery charge to use electric mode. Why is this happening? My guess, the electric system is too hot and needs to cool down, and sure enough, after I park the vehicle for some time and drive it again, it behaves normally.
Back to the big hill scenario, if my theory is correct, as I descend the hill the drive battery gets fully charged, and the entire electric system heats up. Reaching the bottom of the hill at a stop light and standstill, there is no airflow to cool anything, exacerbating the temperature situation. The system knows the drive battery is fully charged and there is no reason to run the engine, so it shuts off, only to re-awaken due to the temperature threshold being too high for electric power, and round and round it goes, until the vehicle starts moving and airflow and cooling start to happen where it can behave normally again.
UPDATE: I do believe this is a bug or some defect in the system, since the engine turning on and off every 5-7 seconds is excessive, to the point where I now have had some friends ask "is your car ok?" I have reproduced this behavior in both Eco and non-eco mode, with outside temperatures between 70-80F.