Macon, that can sure 'nuff be a sign of run out but you can sometimes get by with a little bit of it, depending. Often if you see a bit of the diamond that's ok if you see the other end of it not too far away. What is bad is if you have a lot of it and it is pointy and just one side.
For a good ramrod, or arrow for that matter, you need to differentiate from any figure that might be present and the grain. If you know what growth rings look like, what you are looking for is wood that was sawn length wise, or with the grain. Look at the rod on the end and follow the growth rings along the length of the dowel. What you optimally want is for the growth rings or lines to run parallel up the whole length of the stick, just as if you'd drawn parallel lines on a 48" long piece of paper. When you find rods that look good in this way, you can further check the integrity of the wood by holding the dowel in your left fingers and bending the stick over the meat of thumb.
Rifleman's concern is well founded if using dowels for ramrods or arrows that have much run out. I've seen broken arrows sticking out of fellows' forearms and it ain't pretty. But just for myself, I don't believe that good hardwoods are any worse for it than hickory. Using birch arrows properly selected, I've been able to shoot them repeatedly against a barn without breaking.
Just examine the dowel carefully and do the bend test and you should be good to go. On the other hand, I won't trust any wood not to break if you work at it hard enough. I never get a hard loading ball down a half of the way and then lean on it with all my weight. It's one of the reason's I don't use prb combinations that are so tight a short starter is needed.
Luck to ya.
If these lines emerge on the side of the dowel much at all, you have run out and a place for the rod to break.