I used to have, not a click, but a creak, from the rear wheel.
The background of the problem was that I bought an e-road-bike. Because decent e-road-bikes were not available with 36-spoke wheels, I had to purchase a bike having 28-spoke wheels. I thought that because the rear wheel is the most likely wheel to have issues and because the frame was an asymmetric frame (Cannondale AI), 28 spokes might be just enough (normally I prefer 36).
They were not. The front wheel suffered a complete and total loss of spoke tension (probably due to 28 spokes being inadequate for braking loads) and the rear wheel also had few spokes with lost tension.
I asked the bike shop where I bought the bike from to solve the issue. Their "solution" was that they put thread glue into each nipple, gluing it in place (thus making it probably impossible to re-adjust spoke tensions after the glue has dried), and tensioned each spoke to a varying not-so-high tension. Thus, I can by plucking the spokes to see that their tension is neither high nor equal.
The thread glue did in fact prevent subsequent tension loss but the rear wheel creaks when I pedal with great force uphill.
I decided that those wheels will never be good and built a wheelset with 36 spokes each (triple butted 2.34mm/1.8mm/2.0mm), a rim with double eyelets and hubs with cup and cone bearings (as opposed to the half-complement industrial non-bike bearings on the original wheelset).
The new rear wheel never creaks when riding hard uphill. The old rear wheel still has the creaking problem, and probably can never be fixed due to the thread glue.
So, your issue could be that rear wheel has a non-equal or non-high spoke tension.