Extraction of small rank unipotent elements in $\mathrm{SO}(2\ell,K)$

The paper continues the series of papers of N.A. Vavilov and the author devoted to the geometry of microweight tori in extended Chevalley groups. It is proved that the subgroup, generated by a pair of microweight tori of type $\bar\omega_1$ in a Chevalley group of type $\mathrm{D}_\ell$, contains unipotent elements of rank less than or equal to 4 provided that the field has at least 19 elements. These unipotent elements are either a root unipotent element or the product of two root unipotent elements corresponding to orthogonal roots.