This has been driving me crazy. After my post, I Googled it and discovered many, many postings on multiple Mac focused sites complaining about this issue - AND, going back to the 2011 MBA. I even found posts back to the iBook in 2002 with the same issue.
Three suggestions that I read and that I tried last night, amazed me. They all worked.
1. Put your left hand finger(s) beside the trackpad on the MBA-cover (to get in metallic contact), and move the cursor with your right finger on the trackpad. Amazingly, the cursor will function correctly,!! But it's no real solution to the problem.
2. Unplugged the charging cable and the cursor functions correctly!!
3. Licked fingers to moisten, then wiped them on his jeans and then the cursor would function correctly!!
Another poster stated that it was a “static” problem. These three suggestions point to a “static” problem and, perhaps, the static problem occurs when the unit is plugged in and charging. Last night I was trying to place an emoji in a post and it was going to another place in the text...this confirms the static issue with me…I was making the post with my iPhone - THAT WAS PLUGGED IN AND CHARGING !! When I unplugged it, the cursor behaved normally. (I'm writing this post with my left hand on the MBA next to the trackpad. I guess it's grounding the computer?)