Strange clicking in lower gears



I drive a '99 Honda Civic LX that has recently been clicking. It clicks most often when I’m accelerating in lower gears (1 and 2 most of all, sometimes 3) and when the car is cold.

I took it to a mechanic who heard it on the first test drive (and told me he’d never heard anything like it) but then brought an engine specialist in to listen during the second test drive because he thought it was coming from the engine. That time neither of them heard anything. They think the problem is mechanical but were not particularly worried. They were recommending that I leave it over night at some point in the future so that they can start it cold and listen for it again.

If it’s just an older car noise (the car has 107,000 miles on it), I don’t mind leaving it be. Does anyone have any idea about it what it might be?