Okay, I see what’s going on here. TextEdit’s behavior is making a lot more sense to me now.
First of all, the split cursor in TextEdit is actually almost certainly on purpose. When you start typing characters in an RTL script in the middle of an LTR line, any successive RTL characters are added in RTL order. But the moment you type a space or a Latin character, both TextEdit and Pages jump the cursor to the right of the RTL string and resume typing in normal LTR mode. So the split cursor means “If the next thing you type is RTL, it goes on this side, but if not, it goes on the other.”
In TaskPaper 220.127.116.11, the cursor just disappears, so the split cursor behavior from build 203 is probably the correct behavior.
BUT, the disappearing cursor is not actually my main problem, it was just the simplest aspect to describe. The actual problem is when I use Shift+Arrow keys to select text around the Hebrew letters. TextEdit and Pages get this right, but TaskPaper does very weird stuff.
To replicate, type several lines of normal English, then put a few Hebrew characters at the end of a line. Then, with your cursor at the end of the line (and invisible), hold Shift and keep arrowing to the left. At random–seeming points, the right end of the selection will jump to the left a whole bunch of characters, deselecting stuff that was originally selected.