My Climbing Onion died back while we were away because the plant sitter missed it. However, this has happened before, and the thing always sprouts again in the spring, but I don't want to wait that long. Would it be possible to sprout this year? Is there a fertilizer balance to use (N-P-K), use grow-lights, a heating pad, et al are available to me.
There's nothing you can do; in fact, according to this https://www.gardeningknowhow.com/houseplants/climbing-onion/growing-climbing-onion-plants.htm, unless moderate moisture and warmth is maintained, its normal for these plants to die down in late summer. If that happens (as it has) then its best to leave it alone and wait for signs of life again, which should be fall, before resuming watering as normal. There's certainly no point in giving it fertilizer now its dormant, nor extra heat because high temperatures may also trigger dormancy.