Honda ST1300A/rear shock preload

The Maintenance Items Needed for a New (old) Bike document from the ST-Owners forum says:

Check the rear shock preload adjuster.

While not described in the Honda Service Manual, the preload adjuster is most likely low on fluid and is not working properly. After unscrewing the knob all the way, if resistance is not felt within two clicks, fluid needs to be added. This is discussed in several threads.

Preload

• Use a light hydraulic jack oil or motorcycle fork oil
• There are (approximately?) 36 clicks in the preload cylinder from zero to full preload, 180 degrees per click
• A couple of the ST-Owners posts ST1300 preload fluid replacement
• ST1300 - Rear suspension / Resetting the preload adjustor

While you do not need to remove the adjuster knob, it's likely that there is gunk in the ball bearing and spring housing plus the threads. By removing the knob from the preload cylinder (after detaching it from the bike is probably easiest to catch the ball bearing) you can quickly clean away any such grime to get the best function out of the adjuster.

Rebound and damping

More about tuning the rear suspension.