Chosen Solution
After battery replacement with iFixit 2012 MacBook Air battery, trackpad is not working now.
Hi guys, just to close this out. When I replaced the battery, I mistakenly removed the trackpad setting screw. (in the front middle) when I realized my mistake, then I didn’t know how to reset it. By trial and error, I reset it so that the head was exactly flush with the surface. Do Not tighten this screw, it is a setting screw. Flush with surface got the trackpad working perfectly. Thanks to you all for your support.
There are two possibilities here: You either have damaged the uppercase cable. Or the trackpad its self has failed. Here’s the IFIXIT guide you’ll need to follow to get to both MacBook Air 13" Mid 2012 Trackpad Replacement. Jump to step 6 to see the upper case cable MacBook Air 13" (Mid 2011-Mid 2012) Trackpad Cable and here’s the trackpad MacBook Air 13" (Mid 2012) Trackpad