Phase transitions of linear multivalent proteins control the reversible formation of many intracellular membraneless bodies. Specific non-covalent crosslinks involving domains/motifs lead to system-spanning networks referred to as gels. Gelation transitions can occur with or without phase separation. In gelation driven by phase separation multivalent proteins and their ligands condense into dense droplets, and gels form within droplets. System spanning networks can also form without a condensation or demixing of proteins into droplets. Gelation driven by phase separation requires lower protein concentrations, and seems to be the biologically preferred mechanism for forming membraneless bodies. Here, we use coarse-grained computer simulations and the theory of associative polymers to uncover the physical properties of intrinsically disordered linkers that determine the extent to which gelation of linear multivalent proteins is driven by phase separation. Our findings are relevant for understanding how sequence-encoded information in disordered linkers influences phase transitions of multivalent proteins.