If it is leaking - and I think it is - you're not going to see a puddle, you'd be lucky to even see a "stain".
First we're talking maybe half a cup of fuel in the float bowl, and when the engine is off, and the fuel pump stops, that it, the most that can leak out is what ever is in the bowl plus whatever is in the line between the pump and the carb - not very much, and probably not enough to be seen.
Second - this is a very slow leak - not big enough to drain that "half a cup" in the space of a few hours - it's going to be a slow one drop at a time type leak.
Why do I think it's leaking? Because I've had this problem myself - not on a Sami, but on a classic Mini with an HS-2 SU carburettor - on which the jet connects to the bottom of the float bowl with a little flex hose, and a rubber washer behind a gland nut, and when that rubber washer leaks, you don't see the leak, you just know that you have trouble starting.
By the way - an electric fuel pump will get rid of the problem - when you switch the ignition on the pump will fill the line and the float bowl even before you crank the engine. It doesn't fix the problem, but it hides the symptom.
I took a look at the parts manual - you didn't mention what year you have, so I picked at random - the '86-88 Samurai carburettor has two "drain plugs" on the side which have to be removed to reach the main jets - run the engine and switch off and then run your fingers over the plugs, see if there is any "dampness" - make sure those plugs are tight.