"You'll only find autotrim on scarebuses."
...and just about every other modern jet aircraft. By modern, I mean in the last 40 or so years.
For example, on the 747-400:
Trim is active with the autopilot off or on. There are various modes...
"Speed Trim" is active at lower speeds, when the A/P is off. The trim runs to oppose changes in speed.
"Auto Trim" is active when the autopilot is on, trimming in response to elevator commands being given for a certain period of time by the A/P. During autoland, trim response is not delayed and responds almost instantaneously to elevator commands.
On a 400, you won't hear the trim running (no clicker), but the "pointer" in the Stab Trim indicator still moves.
Rgds.
Q.