Not sure it's the same you mean, as I think the text cursor thingie (I beam) is used as "draw a time selection" cursor, not only in envelope lanes.
Here's a page with all(?) known Reaper cursors and their names:
http://www.reaper.fm/sdk/cursors/cursors.php
If you have a valid cursor icon file called "arrange_ibeam.cur" in the "Cursors" Folder of Reaper's User data directory, Reaper will use that instead of the system icon. I use
RealWorld Cursor editor, which is free of charge (but you're invited to donate). For no other particular reason. It's just the first one I tried
.