what brand name terminal are you using, you can look into it to see if it has a config setting for the cursor to not blink, or be the bar | instead of a block or even to not show it.
if it is straight off the tty login.
turns off cursor .
Code:
echo -e '\033[?17;0;0c' > /dev/tty3
place that into a file then make it executable
no need for shebang, then from whatever filename you gave it, after you changed it to whatever tty you're using, then run it.
kills the cursor.