I was about to call an electrician after hearing a faint click every 10 seconds for three nights straight from the attic. Turns out it was just a loose wire in a junction box near the furnace vibrating when the AC kicked on. Tightened the screw with a #2 flathead and the noise stopped completely. Has anyone else had phantom sounds that ended up being some simple fix like that?
That hum could also be a loose pipe strap or a faulty pressure relief valve. I've got a similar thing in my house in Austin, but mine turned out to be the washing machine drain line banging against the wall during the spin cycle. Drove me nuts for six months before I figured it out. It's wild how we just accept certain noises as part of living somewhere.