The situation is, two forces are fighting each other in a war, while you are doing nothing. The intention is to let them destroy or weaken each other before you make a move.
Any verb or verb phrase for this? "Waiting" isn't good enough, and "biding time" doesn't have the right connotations because it's too general. Also, the notion of neutrality isn't good enough either, because usually you think of neutral nations as having no intention to enter the war (or at least not as a major player but possibly a tag-along ally).
I swear when I first tried to think of this, I came up with "dinkering". Onomatopoeically it somehow seemed right, but it doesn't appear to even exist.
Best Answer
As for dinkering, you may have been thinking of the slang phrase dinking around (unfortunately, I can only provide a link to the Urban Dictionary) or the word tinkering—or some combination of the two.
But an expression for the situation you describe is playing both ends against the middle.
It's often used where the "person in the middle" actively manipulates both sides (think of the Japanese movie Yojimbo and its English remake A Fistful of Dollars), but it can also be used when somebody doesn't necessarily do anything ahead of time but still waits to take their own action against the weakened victor.