Sounds like it needs the breather cleaned out and checking.. There' a restrictor in most of them, and, running up under the gear shift cover there is a breather pipe that can get squashed somehow.. Can't remember exactly but I've found them clamped down under the shift or the covers or something..

starts and seems to run good, but has to warm up a bit first. It jumps when put in gear, but i've read at serveral places that a Big Bear is notorious for hard shifting and a slight jump when puit in gear. two thing i need for it is the fan motor controller, which i ordered, and eventually a pull start assembly and it's 100% done

When you are doing that rev test, don't let it get to an idle, and don't hold it at the revs either. The motor has to be constantly either accelerating or decelerating. From near idle speed, up to revs and back down again should take about.. err.. one to one and a half seconds.. Only give it light throttle, but snap the throttle shut. At the right combination it will start smoking.. Find the right combination and then stick to that for thirty seconds and it will get worse and worse.

It would appear to be the rings are worn, but before ripping it apart I'd check the engine breather system. First thing is check if the crankcase is pressurinsing. Idle it for a few minutes and then take the filler cap off and see if it puffs out air as it comes off. Put the cap on and run it or take it foe a ride and then with the motor stopped undo the filler and check for pressure. It's common to have a very small amount of pressure in there, but it shouldn't hiss or push on the cap at all as you take it off. With the cap off and the warm engine idling, check to see if it's puffing much air and oil out.. A bit of oil splashing is normal. There is a restriction in the breather that can block and cause either excessive pressure while it's running or even, if it's bad, residual pressure in the crankcase. If the breather is clean, and if in doubt you should clean it, including the restriction that will be in the breather pipe somewhere I think. The restriction is sometimes under or in the air box, then, give the motor a few repeated revs. You want to open the throttle much slower than you were in those videos, but let the revs build to about the revs in the video, then as soon as it's up to revs close the throttle right off suddenly, when it gets near idle revs, but without letting it idle, give it a bit of throttle again till the revs build to the video revs. Keep doing that repeatedly and if you get the throttle opening speed and amount right, and the revs it goes to right, it will start smoking if it's the rings, and the more you do it, the worse the smoke will get. Try different amounts of throttle opening speed and amount, and revs, at some point it will start smoking bad if it's the rings. The revs in the video are the highest you want to go to, probably a little less will work better. I've bought cars for people cheap by showing the owner how much it smokes.. haha..

Have you looked in the manuals section of this site ? Owner manuals are often available in pdf form for free from the dealers/manufacturers.. Or, look on goggle... They will be out there.