The thickening base commonly used in Japanese curry sauce is roux.
Japanese curry roux is made by combining fat, flour, curry powder, and other seasonings. The mixture is stirred into a stew of meat and vegetables, where the flour thickens the liquid and gives the sauce its smooth, glossy consistency. Home cooks commonly use commercial roux blocks or powdered mixes rather than making the base from scratch.
Japanese curry developed after curry was introduced through Western influence, especially via the British, and it became distinct from many South Asian curries. It is usually milder, sweeter, and thicker, and is often served with rice as kare raisu. Potatoes, carrots, and onions are frequent additions; tonkatsu served with curry is called katsu curry.
Miso paste can add savoury depth, but it is not the standard thickening base. Gelatin may thicken when chilled, and corn syrup mainly sweetens, so neither is the canonical answer.