Construct the delta-neutral position in the question: buy the 0.5 and sell two of the delta 0.25. Then consider the position's payout as a function of the underlying just before expiry. Its maximum then lies close to the strike of the delta 0.25 where the position's delta then will be zero.
Now, as time to expiry increases (we go backward in time!) the value function smears out as illustrated in the diagram (red to purple). Still though, the point were the delta is zero will be at the value function's maximum. However handwavy this is, it goes well with intuition. Going further backwards in time we will hit the current point where the long call is delta 0.5 and the two short calls are delta 0.25 where the underlying is at the strike of the delta 0.5.
Here we have delta = 0 still at the max and hence gamma and vega negative.