How can find out the right paint to handle this unpainted gap?
There are two problems:


Matching the original color


This generally involves finding some documentation - which you say you don't have - of the original paint. That is not at all unusual. But if you could find that original color then you could go to a paint store and they could mix up a small container to match the same basic specification. Paint stores only stock a few colors (like "white"). Everything else is mixed to order. However, mixing is not entirely perfect, especially with a small batch (less room for error in the proportions of different colors), and there are also variations between paint manufacturers, so that two nominally identical colors from different manufacturers may appear slightly different.


Matching the current color


Paint color (and fabric color and carpet color, etc.) changes over time due to weathering and other factors. So what you often want to do is match the current color because what you are really trying to do is make everything - old and new - look the same.

The usual way to match a paint color is to take a sample to a paint store, where they can scan it and then produce a paint to match it. That is easy if you have any removable painted pieces - whether chips starting to peel off or a piece of lumber that can be temporarily removed from the rest of the structure. If that is not the case then you are left with the final option:


Paint Color Chips/Samples/Fan Decks


A professional painter will walk into your house with something like this:



and let you pick the new colors for all your rooms.

Buying a fan deck for one little job doesn't make sense. But many paint stores will have samples or color chips or individual pages from these decks available for customers to take home, whether to match an existing paint color or to help pick a new paint color for any reason at all.*

With the picture of your existing paint, pick up a range of chips that seem to be close, then go home and see what is closest - a typical digital picture does not show exactly the same colors as the real object.

With any of these possible solutions, keep in mind that paint looks different wet vs. dry. On the one hand, it may not look quite right initially but when dry look like a very good match, but the reverse is also possible. But for a small area like this, "close enough" is probably "good enough" until you feel like repainting everything at one time.



*My wife (fiance at the time) wanted to tell her bridesmaids what color to use for their dresses. We went to Home Depot and picked out some sample color chips. (All kind of looked the same to me...)