Under what circumstances would azeotrope exist in non ideal solutions? (when would the dew point curve and the bubble point curve meet?)
Azeotropes do not exist for all non-ideal solvent solutions. All solvent solutions are more or less non-ideal, but not all solvent combinations form azeotropes. 

E.g. ethanol and isopropanol form azeotropes with water, but methanol does not.

Azeotropes exist if there is large enough deviation from the Raoult law. It means if the azeotrope point of the diagram is pushed enough away from the endpoint connections. 

For near ideal solutions, like n-pentane + n-hexane. there is no bottleneck and onle one convex/concave chart segment. 

Back to the meeting of boiling and condensation curves, they meet at the pure solvent points and eventually at the azeotrope point, if it exists.



Existance of such minimums ( or maximums ) ob the vapour diagram means there is an azeotrope. An azeotrope behaves like if it were the 3rd substance, with  the same composition of liquid and vapour above it, so the curves meet there. 

Minimums meet if and only if liquid and vapour compositions are the same. That happens if and only if either the liquid is pure solvent either it has the composition of the azeotrope ( if it exists ). 

You can create simulations yourself by defining nonideal vapour pressure equations as $p_i(T)&lt;&gt;p_{i,0}(T) \cdot x_i$. It cannot be exactly calculated, as neither the mixture of pure solvent and azeotropic mixture has the ideas behaviour.