Sorry to take so long in getting back to you. (It may be as long again before I try to see if another book in my collection has anything relevant, though.)
Angus Sinclair's <i>Development of the Locomotive Engine</i> (New York, Angus Sinclair Publishing Company(*), 1907; new edition with annotations and afterword by John H. White, Jr.(**), MIT Press 1970: Interlibrary Loan is your friend!) has a 50 page chapter on valve gears… which doesn't mention Norris. But I think it's relevant anyway.
(1) There's a paragraph (p. 446 of 1970 edition) that begins "It seems strange for a twentieth century engineer to reflect upon, but it is a fact that the pioneer engineers had very vague ideas about the advantage of steam expansion and how expansion could be most readily secured. This was curious for Watt had invented an indicator to show the practical action of expanding steam." And goes on to give some examples. It appears that locomotive designers in the period of the early Norris engines really were content with "one speed forward, one speed back" valve gears giving essentially constant cut-off. From our point of view this is maybe a good thing: it means that, in trying to imagine what a Norris 4-2-0 of the 1830s had, we can imagine the simplest and crudest arrangement imaginable in the confidence that it might in fact be right! (Grin!)
(2) There are some drawings of early valve gears: the clearest perhaps on p. 449, captioned "Common Form of V-Hook Motion." Start with two eccentrics on the axle. (Given the small forces on these early engines, they can be pretty narrow and, since they are side by side, can operate connecting rods that aren't in too different planes from each other.) One is for forward motion, one for backward. There are rods (I'll call them rods, anyway) running from the eccentrics to the lower pin of a rocker whose upper pin actuates the valve rod (= extension of valve stem). The rod for forward motion is angled up, so its hook end (= the end away from the eccentric) is above the pin on the rocker, the one for backward motion angles down, so its hook end is below that pin. The upper (forward motion) rod has, as its "hook," an inverted V shaped fork, and the lower a right-side-up V. The reversing gear involves a lifting lever that lifts the two eccentric-to-rocker rods simultaneously. To go forward, lower it and the upper, inverted, V slips over the pin on the rocker and rests on it. (The open end of the V means that it will catch the pin on the rocker even if not lowered very precisely over it. The apex of the V has a slot so, once engaged, the pin on the rocker has more or less vertical surfaces in front of it and behind it, so it won't tend to slide out as it would if in contact with the slanted legs of the V.) To go back, lift the rods so the forward-motion hook is freed and the V of the backward-motion hook engages. … Since one probably wants to go frontward more than backward, it makes sense for the foreword-motion rod to be the upper one: gravity will help keep it engaged. … … Crude and probably very inefficient, but the only valve-gear arrangement simple enough for me to understand it on a first look at the diagram!
(*) I think Sinclair ran what was basically a proprietary railroad correspondence school, and he published lots of educational matter. Including a drawing -- included as a fold-out inside the back cover of the 1970 edition of the book -- of a 4-8-2 locomotive with 385 parts numbered and identified.
(**) Was the curator of the Smithsonian's Museum of History and Technology. Wrote many things on the history of steam locomotives.