Apologies to folks who already know this...
First, a 98.5 Dodge truck isn't really a "thing", just like a 64.5 Mustang or a 70.5 Camaro are just a convenient way for marketing people or enthusiasts to refer to a significant difference. The 1/2 does not appear on a title.
The emissions requirements that led to the 24v introduction said that engines that did not conform to the new regs could not be installed in trucks after 12/31/97. So that's when the 12v trucks stopped and the 24v started the next day. Or due to holidays and/or production-changeover logistics, the 12v may have stopped a little sooner and the 24v started a little later, I don't know.
Federal rules for model year designations say you can identify a particular model year pretty much whenever you want, but that designation can not be used for production during more than one January. You could start 2017 production in Feb 2016, build it all of 2016, cross into January 2017 (the first time it was built in any January) and keep going thru December 2017, ceasing before the next January comes around. Not that you'd want to, but it's legal.
To make it even more extreme, you could start building 2020 models in Jan 2017, but you'd have to stop before Jan 2018. Then what would you do?
As for rarity, I don't know the build-quantity breakdown of engine/chassis/cab/bed combinations, but the thing that makes the 98.5 special is the quad cab started at whatever the beginning of 1998 MY production was, and could be gotten with a 12v only until December 97. So if you prefer a 12v engine but want back doors, those few months are the only ones there are. There was a recent discussion of whether short bed or long bed, or 2wd or 4wd was the "Holy Grail," but I reckon your personal Grail is whichever one you want. For me, at home in FLorida, it'd be a long bed 2wd. When I'm in New York it'd have 4wd, but they're all too damn big to park anywhere unless you have a good reason to own a big truck, and in New York, I don't need it.
If you want a standard cab 12v, there's no important difference between a 98 and all the years before it, and if you want a 24v, there's no important difference between a 98.5 and later trucks other than optional HP choices, 6sp vs 5sp manuals, and disc brakes.
Edit to properly respond to the actual question: Model year 1998 did not end in Dec or Jan. It started and ended at Dodge's normal times to start and end, whatever those are. "98.5" isn't a model year. Installation of 12v engines stopped no later than 12/31/97.