Thermoquad base gasket leak

What is your carb leaking?
A carb is not supposed to leak, period. If your carb is leaking gas, there is something wrong with it,period.
The base gasket is not meant to stop gas leakage, the molecules of gas will seep thru places that air will not flow.
There are only three ways that gas will come out of the base gasket of a non-running engine; 1) up over the bowl,or 2) out the bottom of the bowl, or 3) thru a crack in the bowl; and you guessed it, none is normal.
With the engine recently turned off, if the gas continues to appear at the base gasket, I'll bet it's coming out the bottom. AFAIK, this only happens with TQs.. because they have their mainwells bonded to the underside of the bowl.
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Judging by how dirty your intake plenum is,either your cam has a very late closing intake valve,or your idlespeed is too slow for it, or the carb has been leaking into the intake for quite a while.

I highly recommend you check your crankcase for gas in the oil, cuz from the intake, there are only three ways for the gas to get out of the plenum; 1) by evaporation straight up past the semi closed throttle blades or sideways from there thru the base gasket, or 2) into the valley thru a leaky intake to head gasket, or 3) into the cylinder thru open intake valves. From the cylinders, there are only two ways out; 1) by evaporation thru an open exhaust valve, or 2) by gravity, sneaking thru the ring gaps and into the oilpan.
Once the oil has been washed of the cylinder walls, the engine becomes very difficult to start.

I never use either, because if the engine doesn't start right up, subsequent tries just destroys the ring seal. I use a mixture of gas and 5% two-cycle oil. A cold 360 cuber will accept quite a bit of raw gas in the intake, just give it a few seconds to make vapors. And when you crank, keep the throttle open until the Rs hit ~2000, before slowly lifting, else she may flood/stall when the puddle comes thru; and then yur plugs will be too wet to start any time soon.
Good luck