Something to remember with caulk is that you need a certain bead width to accommodate a certain amount of movement. Wood expands and contracts seasonally. A 1mm wide bead of caulk would need to stretch 100% to stay intact if the 1mm gap becomes 2mm in winter when the wood dries out. Most caulks can’t do that, and will crack. A 3mm or 1/8” wide bead of caulk is more likely to be able to stretch by 1mm up to 4mm without breaking. So in a serious way, caulk is better at filling BIG gaps, and a poor solution when the fit is quite close. Check the expansion rating for the product, and think about how that relates to the movement of the gap you’re trying to fill.