As long as you are outside the FAF, and haven't captured the GP/GS, it is pretty simple to accommodate a request to fly a "360 for spacing", especially if you are still in altitude hold.
For this approach I arrive at the SOKYO IAF at 3,100 ft in altitude hold, and stay at that altitude through the procedure turn until intercepting the glidepath prior to the ROKSE FAF.
If the tower requests a 360 for spacing just as you report inbound on the procedure turn outside of the IAF, leave your navigator alone, and simply reach up and press the autopilot TRK button. You can also use the HDG button, but make sure to push in on the HDG/TRK knob first to sync selected HDG to current HDG.
Next, just use the HDG/TRK knob to turn the plane left or right and the autopilot will follow the HDG/TRK bug, and fly a perfect standard rate turn back around to the approach course. As the plane is coming around the turn on a path to intercept the approach course, just press the APR button and the autopilot will resume the approach right where you left off.
As another example, if the tower requests a 360 for spacing as you report the IAF inbound, the system will have just transitioned to the FAF being the active waypoint (in this example approach), but that is also fine. Just do the same thing using the TRK and APR buttons to circle and then re-capture the approach course.
As mentioned earlier, you can't circle after capturing the glidepath/glideslope, or the navigator will annunciate an approach error condition.