>> Console Player here too <<
Hold down L1 + R3 (right joystick). This turns on the mouse mode. One of the joysticks moves the cursor around (I think R3). Holding down (either L1 or L2, can't remember which) lets you highlight text, but only from the chat box.
Unfortunately, you can't highlight/copy text from other peoples search info or adventures plates.
(I could be mistaken about some of the buttons)