When I used chain oil I'd wet clean about once a month with a spinny brush reservoir doodad, then follow up the water based solvent with WD-40, then oil (Park CL-1 or Tri-Flow). No rust. Lots of gunky grit accumulation.
I switched to wax -- melted Gulf paraffin -- last year. No more cleaning to speak of. Once in awhile I'll wipe down the chain with a dry paper towel, leftover napkin, whatever I have in my pocket.
Once a month I swap chains, between two identical KMC Z72 chains with Missing Links. The "old" chain goes back into the crock pot of melted wax. Then hang to drip dry.
There was always a residue of wax, so no rust problems -- although we don't get a lot of rain and I don't ride much in heavy rain.
Recently I was curious to try reducing the wax residue, so after the freshly waxed chain cooled enough to handle I wiped it down with a rag soaked in mineral spirits. The chain felt like bare metal, no waxy residue, and it has less friction on the bike. I was concerned about whether it would rust and whether I'd need to swap chains more often than once a month/every 400-500 miles.
So far, so good, although it's been only two weeks now. But I've ridden in light rain and through puddles. No rust. Feels like a bit less drag on the drivetrain than when I left a heavy wax residue, but I'm not actually any faster. It just *feels* less draggy on hill climbs. But I'm a slug on climbs so anything that feels better at least gives me a psychological boost. I'll take it.