Can I trace just one part of an image?
Yes. Magic trace in Vectornation by Zaweba lets you click the parts of a picture to trace, with Shift to add areas and Alt to take them away.

Yes, and you don't have to trace the whole picture to do it. Vectornation by Zaweba has Magic trace, which lets you pick the parts of a placed image you want as vectors. Hover to see the area it will take, click to trace it, hold Shift to add more areas and Alt to take some away, then press Enter to create the shape.
That is a different way of working from Image Trace, which turns the whole picture into shapes at once. Magic trace is for the times when you only want the logo on a van, the shape of one leaf, or the outline of a product on a busy background.
How Magic trace behaves
Place the picture into your document with File > Place and pick the Magic trace tool. As you move the pointer over the image, the area it would trace shows up, so you can see what a click will catch before you commit. Click and that area is traced.
Building up a selection is where the modifier keys come in. Hold Shift and click to add another area to what you already have. Hold Alt and click to subtract an area, which is handy for knocking out a hole such as the middle of a letter O. If a click takes in more than you meant, Ctrl+Z takes it back. When the outline is what you want, press Enter and Vectornation creates the shape as a vector path.
The settings that matter
Three settings shape the result. Tolerance decides how different a neighbouring colour can be and still count as part of the same area. A low tolerance is strict and catches only close colours; a higher one spreads further. Start low and raise it if the area stops short.
Stop at edges keeps the selection from leaking across a visible boundary into the next region, which helps on photos where colours are similar on both sides of an edge.
Background mode is for the opposite job. Sometimes the easiest thing to click is the background, and the thing you want is what's left. Use it when the subject is complicated but the background is plain.
Where it helps most
Logos on photos are the classic case. You have a picture of a shop sign or a printed bag and you want just the mark, clean. Click the parts of the logo, add the pieces you missed with Shift, take out the counters with Alt and you have it.
It's also useful for pulling a silhouette from a product shot to use as a cutting line or a shadow shape, or for picking flat colour areas out of an illustration one at a time so each becomes its own shape with its own fill.
When to use full Image Trace instead
If you want the whole image as vectors, Image Trace is quicker and gives you more control over colours and smoothness. It traces shapes rather than pixels, keeps corners sharp, snaps near perfect circles and lines to exact ones, and its Abutting setting makes neighbouring shapes share edges with no gaps. Magic trace is the precise, piece by piece option; Image Trace is the whole picture option.
The two work well together. Trace a whole illustration with Image Trace, then use Magic trace on the original picture to add back a detail that got merged away.
A final check
Once your shapes are created, hide the placed image and look at the vector version on its own. Small slivers and rough edges are easier to spot without the photo behind them. The path clean up commands under Object > Path, such as smooth and simplify, will tidy any edges that followed the pixels a little too closely.
Tracing just the part you need keeps a file light and saves deleting dozens of unwanted shapes afterwards. In Vectornation by Zaweba it is a few clicks and an Enter.