I would recommend finding a map that you like (or an area here on Earth that's about the same size) and seeing what others would show for it. Ultimately, as Midgardsormr pointed out, you should show the rivers that are important to why the map exists! Historically, maps were done for a purpose. Keep in mind why the map is being made when you work on it.

Also, as jbgibson pointed out, some of your rivers are doing things that require special terrain conditions. If you look at a contour map of the world (one with lines at differing heights), rivers almost always cross contour lines at right angles. If you sketch out the rough contours (mountains here, highlands here, hilly here, and so on), you'll find that it will help enormously in placing plausible rivers. It might even help you with how many rivers to show! I did a quick example that shows the opinions of a particular piece of software that moves things downhill:
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You can force rivers to go like that, but the system would really prefer to run rivers more perpendicular to the coast. That map is a bit bigger than Borneo; check how rivers look on maps of that area (keeping in mind that Borneo is a very wet place)