Extraction of small rank unipotent elements in $\mathrm{GL}(4,K)$

In the present paper we prove that in the group $\mathrm{GL}(4,K)$ over the field which has at least 19 elements the subgroup generated by a pair of 2-tori contains unipotent elements of rank 1 or 2. Keeping in mind the papers of N.A. Vavilov and author this result is valid for any general linear group. This paper is one of the first step of studying of the subgroups generated by a pair of microweight tori in Chevalley groups.