I've done all that and the Section38 app just will not come up when searching via Google Play Store. I tried various inputs, "section38, section 38, immigration Thailand, immigration bureau Thailand" and it refuses to display the app.
In the end I used a link provided by Ubonjoe which I've since found out you can also generate yourself via the Play Store once you have the app installed.
It is...
https://play.google.com/store/apps/details?id=th.go.immigration.section38