What's the rhythm of the clicks? Once every wheel revolution? 8 or 9 or 10 times a revolution?

Common causes are valve stem moving within the rim hole. Bearings that are so dry of lube and not tightly adjusted so you can hear as the bearing that is "going over the top" you can hear it fall onto the bearing preceding it. Spokes that are so loose they move against each other at the cross. Spokes that have a notch worn into them at the cross and it clicks as the two spokes flex. Spoke nipples moving within the rim holes. Star/strike style odometers (had to toss this one in for fun). Hub flanges are loose on the barrel and move with side forces.

I'm sure there are more causes. But by figuring out the frequency first you get some elimination of some causes. Placing a small piece of plastic (like cut up bleach bottle) between each spoke crossing can fix these click causes. Lubing hub bearings and spoke nillles can fix those causes. Andy.