Probably not what you are looking for, but as you know LR Classic shows "markers" on the map for all images currently in the film strip, and what is on the filmstrip depends on what source or sources are selected (folders, collections) and what filters are applied (stars, flags, keywords, other metadata, etc.). So, the way to only have one image marker displayed on the map is to only have on image in the film strip. But to make this useful you need a way to control what is on the filmstrip from within the Map Module rather than having to flip back and forth to the Library Module.
Now, in an ideal world there would be a "show active marker only" switch or button someplace in the map module, but there is not that I know of. The second best solution would be a way to change filter settings in the map module, for example, change the filter to Text: file name contains IMG_1234 (assuming that's the image you want to isolate on the map). But, alas, you don't have that option in the Map Module either.
So we're down to a third best option which you can actually do. As it turns out when in the Map Module about the only choice you have as to what's on the filmstrip are collections. So, here's your solution to show only one map marker on the map and to be able to select different images to show without having to exit the Map Module (not optimal but not too bad.)
ONE TIME SET UP:
In the Library Module, create 2 dumb (regular) collections. One called "Working Set" and one called 'Target Image" (use your own names but I'll use these for this answer). I would put these two collections in a collection set called something like "Map Control" so they are next to each other in the collections panel.
1) Get all the images your're interested in, onto the grid & film strip however you wish. and add them to the "Working Set" collection and select that collection as your source.
2) Now go over to the Map module which will show you map markers for all the images in the "Working Set" collection.
3) To see only one image marker on the map, drag that image from the filmstrip to the "Target Image" collection (still in Map Module).
4) Select the "Target Image" collection as the source collection by clicking on it (still in Map Module). Now you'll only see that one image marker on the map
5) To swap to another image, right click on the one image in film strip and select "remove from collection" then re-select the "Working Set" collection and repeat steps 3 & 4.
So, not ideal, but not too bad. And as I'm sure you figured out by now, you can drag more than one image to the "Target Image" collection if you want to see more than one but not all the markers.