I used to hunt them a lot in my youth. That string idea is excellent. My hunting partner and I took turns doing the bushes job while the other waited w gun trained. I used calls to get them to stick their heads up. It rarely drew them in unless they were already IN the area. (Feeding)
A guy in the gun club told me there is a call which imitates a young squirrel in distress call which is supposed to bring them running but haven't we ALL heard SOME form of sage like advice - usually from the Bar end of the club.
22 vs 20 ga.
When I brought a 22, the squirrels w only present a running target. When I brought a shotgun, they would throw a party just out of range and just dance. How they knew which gun I had is one of life's great mysteries. But I ALWAYS swore I was going to get one of those rifle/shotgun combo's just to get even. .