Ok, thanks a lot for your help.
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The switch in the house, (single gang) does have neutral wires available. I see them coiled and wire nutted in the back of the box.
Hi Larry. Welcome to the community. You’re right that there is a neutral in the single-gang, but unfortunately that’s the one in the garage! 
The house box has both the neutral and live, just power the garage lights from that circuit instead…