I’ve got exactly the same situation here, but found the reason: the non drive side pedal.
But it wasn’t so easy: the drive side arm on my venerable Shimano FC-M131 crank cracked around the pedal thread after 10000km or more of reliable service, but it was my fault (hit a concrete slab laying near the curb, the pedal also broke). Took the opportunity to make a complete replacement of the drivetrain: new crankset, chain, cassete (these from SunRace) and derailleurs (from Shimano). And so a dilemma begins...
Unrelated to the original problem, I’ve managed to crack my old frame and took the opportunity to change the bottom bracket (Shimano UN-BB26, same as previous). But I’ve found SunRace hasn’t an effective quality control: the crankset’s square hole was off center by a tiny amount, enough to cause some rubbing on the front derailleur (thought it was due to the old bottom bracket, but the new one was installed and the problem persisted).
Coincidently to the bottom bracket replacement, I’d noticed an annoying clicking sound every turn on the pedals. Thought it was a faulty bottom bracket (the seller borrowed me another one to check, nope); thought about more troubles on the crankset, but never could positively identify it; thought it was due to an 8s chain and cassete being mated to a 9s crankset, but can’t prove it...
As you, I couldn’t reproduce the issue out of the pedals. To my despair, my wife took the bike for a ride and found no clicking at all! Thought about a problem with the new frame (I’m quite heavy at 120kg, so I thought that was the problem), but couldn’t find any crack on it.
Out of the blue, the clicks started to get more frequent. I went commando and started to test random things, exchanging parts with my wife’s bike. When I exchanged the pedals, the problem was gone, but that wasn’t the end.
Took the pedals where I bought then, the seller is one of my trusted mechanics, (the same who sold me the bottom bracket) and he replaced them at no cost. After only about 2km down, there was the annoying clicking again! Came back there and begun to test one pedal after another, just to find the complete batch clicked out of the package or after a couple of kilometers!
Curiously, they only clicked with me, my mechanic is almost featherweight at just 60kg (little more than half my weight). He agreed to disassemble then and make a complete overhaul and repacking of grease on both pedals. Hadn’t ride as much as before, due to coronavirus and rain season, but whenever I’d ride, there’s no more clicks.
Just for laughs, I was about to christen the bike TicTac, but not anymore...🤣🤣🤣🤣