I got lucky and found the service manual. On the FS600V, set up for recoil start, there is a stator under the flywheel and it appears to have a single wire. I'll put the mover back together, get it started and check the voltage at the single wire from the stator.
Also, per the service manual, the recoil stator should have resistance 4.4 to 15 ohms. Given that it's a single wire stator, do I check the resistance between the single wire and a ground point?