The Black Powder rulebook has two pages on rockets (p 84-85). It states that "Rockets are provided with frames for firing and each frame together with its crew, limber and horses forms a unit".
This is not quite the whole picture for the British rocket system. I have an excellent (and cheap) reprint of Congreve's original manual, which I purchased at the Royal Artillery Museum a few years ago. Most of the illustrations you will see in other publications of this system are copied from this book.
A British Rocket Troop (ie battery) had 6 rocket cars, each pulled by a normal team and limber, so were exactly the same size as any other RHA Troop. The rocket cars were based on the same Desaguliers design as the artillery limbers but had two long boxes on the sides (for rocket sticks) and a short box in the centre (for the rocket heads), so that in plan view they would form an "H" shape. If anyone has seen the plastic 1:72 Hat model of a simlpe cart, it is incorrect. Two firing frames were carried, one on each side of the rocket car, and rockets could be launched with the frame still attached to its rocket car or separated. Firing from frames was used for the heavier rockets (12 - 32 pounders). The rules in Black Powder fit this completely.
There was however a light rocket system also carried by the Rocket Troops. All of the men in the Troop were mounted, unlike a normal RHA Troop where a proportion had to ride on the limbers. Each Rocket Troop artilleryman carried 4 x 6 pound rockets in holsters on the front of their saddle (two on each side) and these artillerymen also carried 4 x rocket sticks slung under their arms, looking not unlike lancers. Indeed they even put a white over blue pennant on them to further this illusion (as shown in the Hamilton-Smith print). The rocket artillerymen therefore had the option of using the rocket cars to fire the heavier rockets or deploying forward with mounted men only to fire their light rockets. The rocket artillerymen operated in six sections (sub-divisions) of 15 men, divided into five teams of three men, one of each team of three carrying a small metal trough on the rear of his saddle, from which these light rockets could be launched.
I always have alternate mounted and dismounted figures for my wargame horse artillery, and have the same number of artillerymen as there were real guns, or in this case rocket cars, in each battery (ie six for British). I would suggest that the Black Powder rocket rules could have a simple addition to allow the mounted rocketeers to deploy forward, without their limber and therefore be able to launch their light rockets (which I suggest should have a range of 48 inches). This is actually what happened during the Waterloo Campaign, when Wellingon insisted that the Rocket Troop was equipped with guns rather than their rocket cars, but they were still able to fire their light rockets during the retreat from Quatre Bras and during the Battle of Waterloo itself.
It was also possible to deploy light 6 pounder rockets using "rocket infantry". I am only aware of this being done in the 1812 War, where Royal Marine Artillery deployed on foot with such light rockets. I would have thought that similar rules could apply to them. I think that all light rockets should be able to move and deploy in a single turn, just like horse artillery.
The advantage of deploying the light rockets is that their men, operating effectively as cavalry skirmishers, could go to places which the heavier rocket cars could not, ie across rough ground or over obstacles. This works within the Black Powder terrain rules.