Okay, well, there are too many variables here right now to be sure of what's going on, how bad is the cat? On these Toyotas I just pull out the front 02 and will look in through the 02 opening with a bore scope to see the condition of the cat. You can also do a back pressure test at that location. The max exhaust back pressure is 1-2 PSI and that's all.
The exhaust leak at the gasket is an issue. There are negative and positive pulses in the exhaust so that gasket needs to be replaced. And if the cat has at all started to restrict the substrate, there is going to be back pressure and combustion gases backing up skewing the 02 readings on both upstream and downstream sensors.
The MAF at idle is low, not by much but it is low. 1.8liter engine should be roughly 2g/s or a little more. The cat's state can be at different levels too, it's not broken apart yet completely plugging up the exhaust. If it was you wouldn't be able to get it up to that higher RPMs, or it would be a no start all together. But it can be on its way to melting down. Right now, it's not able to store oxygen and that's why you're seeing the fluctuating rear 02 sensor. The next phase is melt down.
You may be correct on the intake gasket but with so many issues it's difficult to say. That Long Term fuel trim didn't budge at all, but it did when you were revving the throttle forcing exhaust out, clearing some built up combustion gases out.
The positive fuel trim numbers are most likely a combination of things. A vacuum leak causes high positive fuel trim numbers at idle with the throttle plates closed. And the fuel trims will come down when you raise the rpm because manifold pressures start to increase and approach atmospheric pressures. Thats not happening here, the short term was jumping back and forth from 0 to -5%, so it was trying to bring the long term down but couldn't. Probably because there are exhaust positive and negative pulses happening. Thats what it looked like with the back-and-forth short-term trims. I would drop the front of the exhaust and take a look at the front of the cat.
And keep in mind that cylinder misfires are what cause cats to fail. So do the spark plugs too. Check the fuel pressure, make sure it's up to spec. A weak fuel pump will cause positive fuel trims due to lack of fuel pressure/volume. The fuel pumps are really easy to get to on these, they're under the back seat. The seat pulls up from its front and there is access to the pump connectors. There's also a quick disconnect in the engine compartment.
Here is some service info on the exhaust, the code P0133 flow chart, and fuel pressure spec.
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Monday, December 25th, 2023 AT 4:02 PM