Historically, the beam brighness(as in the beam current) is known as 'Z'. You'll find this on the back panel of most CROs.
Normally the 'Z' is used to turn the beam on and off - off when you've moving to a new position, on when you're drawing a vector. Of course, you can drive this with a DAC and have different brightness vectors - this is also achieved by repeating the same vector more than once.

As you mention, if you leave the beam static, the brightness is at it's maximum and decreases the faster you move the beam. The usual characteristic of vector scan is the bright dot at the end of the vectors.

Whenever I tlak about vector scan, I hark back to my younger days on the Asteroids machine. Now I suffer from 'asteroids'!