DIDn't a gal post a similar thing, some time back. and, it turned out to be some pump down the street?

Similar, but different... This OP, as I understand the posts, maintains there's no water pipes in the offendng wall.

I like the "woodpeckers in the attic" scenario. I think the OP should plan on going up into the attic the next time the noise is present.

Similar,..... and it took 15 MONTHS to finish that thread...

.

Noises frequently today, but not quite as bad. Can't rule out anything, but I don't think a woodpecker would disappear and come bac 2 months later, would it? Not sure if plumbing in the wall...it's an exterior wall that faces the north. Suppose tomorrow I should put food coloring in all the the toilets and check for a leak.

A woodpecker has a distinctive "braaap" sound like a
tiny machine gun or engraving pen. Pipes go BANG....BANG..

The nature of the noise might lead you somewhere.

Could it be a loose piece of soffit, or siding, blowing/rattling in the wind? Or the louvers on a whole house fan exhaust?

I'm not feeling the woodpecker scenario since you said it happens most frequently at night. Do you have a heat pump located outside the bedroom wall? A common practice on new homes around here is to mount the AC or heat pump unit on a metal bracket suspended from the foundation rather than setting it on a concrete pad. It allows the HVAC guys to do their job prior to finish grading. If you have this type of setup, compressor start-up noises might be telegraphed through the metal mounting bracket and be picked in the wall or duct work. Just a thought... Good luck.

Woodpecker or not, a look into the attic when the noise is present would be my next move.

Yep. Maybe a raccoon or squirrel(s)...