No 6010, use 6011. It will run them on 20A as it will run 3/32 lo-hi. Only time I have tripped was with long circuits, 200 ft at end of a barn and if I turn it down a pinch and limp a little it will work, never tripped it with the 11 but a couple times with the lo hi but I had it dialed up to toasty. I have heard of guys using 6010 but I am sure they were dragging the rod around, not aggressive whip and pause which for my case is the reason I use it.It will run on a 6000, if I had to use it on a gen set I would tend to use 240 if possible, could use 1/8 lo hi.
When I was at one of the barn jobs found another light 20A 240 circuit, after I connect to that no more issue despite the distance.