Not quite
"When counting at Spanish 21 or blackjack and the running count exactly equals the standing index,"
Did you mean to say the true count?
"does the player benefit more by standing or hitting?"
By definition, mathematically, it doesn't matter, but the concept is that, if the TC EQUALS or exceeds the index, you stand.
"I think I know the answer. Hitting would lower the variance by allowing the possibility of a push. And lower variance is always good for a counter. Do you agree?"
Not quite. Hitting also uses up cards, so, if the index that we're talking about is a positive one, indicating a favorable situation for the player, you would do best not to use up any cards by hitting.
Don