Why does the solution turn from red to brown after boiling with sulfuric acid? Isn't the gold amount so small? How would it become visible?
Gold can colloid in solutions, take for example with where tin is dissolved with gold, the dissolved gold ions will be reduced to gold atoms (we cannot see) many of these atoms of elemental gold are coming into contact with each other and join in clumps (we still cannot see), these clumps come into contact making larger clumps of gold atoms (we cannot see), before growing large enough for us to see this reduced gold clumps will develop a static charge, now they begin to repel from each other (now we have a colloidal gold solution, (we may not be able to see that it is a colloidal solution unless we shine a light through it (Tyndal effect). the colloidal gold is already elemental gold but these clumps will not settle in solution, because of the static charge.
We cannot test for the gold a colloids in the solution, these tests rely upon the gold being an ionic salt and the stannous chloride or ferrous sulfate, in the tests reducing the gold to elemental gold, as a colloidal gold solution of purple of Cassius with stannous chloride, and elemental gold in a brown ring of gold around the ferrous sulfate crystal.
It would depend on how much gold (as colloids) was in solution whether you would see the brown precipitated gold from solution after breaking the colloidal bond, small amounts of gold you would have to search hard to find any sign of gold, but if a fair amount of gold was in solution you could find it easy in the beaker after settling as brown or black powder...
Is there a "safer" way to break the colloid rather than using sulfuric acid to boil?
Electrolysis can be used to break the colloidal bond.
Previously I added a couple of tablespoons in a half cup of colloidal gold. The result was that the solution turned from red to clear.
What would have happened had I boiled it?
Not much, sounds like your gold has precipitated.
You can shine a flashlight through the side of the beaker and look for the Tyndal effect for a colloidal solution...