While configuring GitHub Actions in this repository and attempting to get MAST to compile with both libMesh versions 1.5.1 and 1.6.2 I ran into issues related to handling of the timpi libraries. libMesh version 1.5.1 does not appear utilize timpi directly, whereas it is required for version 1.6.2.
It appears there is a workaround in the cmake/FindlibMesh.cmake file to assign the libMesh libraries to the timpi variables if timpi isn't found (as in the case of v1.5.1). I believe we can handle this better by detecting if libMesh version is >=1.6.0 and make them required.