In this paper, we explore the $(1,2)$-center problem for polygonal curves under continuous Fr\'echet distance. The $(k,\ell)$-center problem, in general, is known to be NP-hard. Aronov, Filtser, Horton, Katz, and Sheikhan (WADS'19) gave a polynomial-time algorithm for the $(1,2)$-center of curves in the plane under the...