I'm having a similar issue. Dropping as low as 400 rpm at idle. Car is a 2012 RAV4 MK3 auto sub 70K miles 2.0 petrol Valvematic, and I've been doing work on it ready to sell after buying a new set of wheels after 9 years of ownership.
It's had a faulty Valvematic controller replaced. New air filter. New NGK Iridium sparks. Few extra bits and bobs around the suspension done. Last job was exhaust flange repair. It was running brilliantly when I took it home, but wouldn't turn over the following morning. Dash didn't even light up. Odd, as previously had no indication the battery was struggling.
Later, I put it on a battery charger. It began at 9.0V rising throughout the day. Once it was charged, it started up first time. After a minute, the revs began to settle as normal. After another minute, the revs dropped really low, almost to a stall. A/C, lights, radio, etc. all switched off.
Checked the battery voltage, and it was a little on the high side, nudging 13V (engine off). Plugged in my scanner and noticed the voltage at the control module was normal when the revs were 13.8V (engine running), so I assume the alternator is working.
Turned everything off. Disconnected the battery. Cleaned every contact I could find across the engine with contact cleaner, including the MAF. Put everything back together, but I'm still seeing very low rpm a couple of minutes after turnover.
Even tried a spare battery, but no change. I'm absolutely stumped. No error codes, so I don't think it's a vacuum leak, as I assume I'd get codes thrown at me.
My apologies for the monologue, but I thought it best to cover everything I know it's not, before asking for help. Does anyone have any experience of this particular issue, and if so, what should I check next?
Many thanks in advance.