I’m looking for any kind of registration number on my late 1900’s specialized stumpjumper. Where do I find it and how to determine build date.
Before you look, you should consider why you need a manufacture date. Here, we argue that the date doesn't matter. You are pretty likely to be able to find replacement parts no matter what the manufacturing date, barring proprietary components. If this is the case, it would be better to specifically say something like I need to repair/replace this thing, what do I do or what will fit? If the issue is restoring the bike for resale, questions about valuation are off topic here, and you also aren't likely to get much for a vintage MTB, given how much technology has changed.
Before you look for the serial number, I suggest reading this question and answers that explain the purpose of serial numbers. If you are hoping to have us identify the bike, be aware that this is impossible with just a serial number, and you would be better off calling Specialized yourself and seeing if they're able/willing to help you. There is no global database of bike serial numbers. There have been some attempts to build one, but the low value compared to automobiles and the lack of insurance coverage means that there's limited incentive to get a consolidated database going.
This site is about asking useful questions and providing useful answers. Questions about identifying a bike from its serial number rarely provide useful information to the community, and they are usually hard to answer (impossible if all we're given is a serial number). You are asking people to put in effort to provide an answer that's informative for one person. The return on investment for the people trying to write an answer is low.
That said, the serial number is usually stamped onto the bottom bracket shell. Look underneath first, then look all around the BB. Full suspension bikes may be a bit more complex, but this is a hardtail.