Toyota Repair: fluctuating RPMs, battery engine, dodge truck

Question
Tim,
Thank you in advance for your advise if you will have any.
I have a 2000 v-6 4 runner auto 86000miles. Always serviced.

Engine light came on. Read code at Advance Auto (po 125).
Reset with reader. Engine light returned in 10 blocks. I had coolant changed and returned to Advance to reset same code. Again engine light returns.
I research internet. Someone in a forum said that code is poorly written and it really refers to the O2 sensor (probably front). I find the part number and buy one from internet dealer. Looks good but plug is wrong even though part number matches. Every parts store brings me correct part with number but all have incorrect plug. I decide to cut old plug off and splice to new sensor. I'm pretty good with that stuff as a low voltage tech. Install the new sensor and then disconnect both battery terminals to clear code while in drive. I reconnect battery, engine starts correctly and voila, no check engine light. Engine runs a bit rough on acceleration. 50 miles later I have noticed a cyclic rpm fluctuation that speeds up with rpms. I went to a mechanic that was referred to me as trusted who said"likely it is the computer re-learning how to adapt to my driving because I dc'd the battery. I can understand that so I decide to drive through the "couple hundred miles of relearning.
I think it should have relearned by now. I'm still having the same problem of mildly rough idle and cyclic rpm fluctuations or "waves". Several times leaving from a stop, the engine bogs down and it only returns to "normal" if I let off the gas a bit. Giving more gas in those situations only causes backfires. I couldn't tell if under hood or in exhaust.
It feels to me like uneven fuel ratio handling.
Ideas? Please.

Answer
Dave
THANKS SO MUCH for telling me the model,year, and miles of your
vehicle !!!!    At least 95% of people don't give me that information
so I don't know if they have a Dodge truck or a Edsel.

When it comes to computer/ECM/PCM's on a vehicle you must use
the exact same sensor that is made for that system, any modifications
and big trouble. If you called a Toyota dealer they would first ask you what your VIN number is so that you get the correct part for that
vehicle.
The first thing I need to know is if your vehicle is a California
vehicle or non-California vehicle. PO125 is DIFFERENT for those 2 type of vehicles.
If it is a non-California vehicle then it is a 02 sensor
that is most likely DIRTY, remove all 02 sensors and clean them
very good with WD-40 and a rag then replace them. Clean and splice back in your old one.

I wish I had $1.00 for every 02 sensor that was replaced on a vehicle
and the old one was just dirty, or the issue was caused by something
else. If I received $1.00 from everyone of those I'd be living on an
island of my own, smoking cigars, and counting the boat loads of my money.

When a 02 sensor signal is sent to the computer and it is out of specs
the vehicle is running rich or lean, this can be caused by many different things under the hood. It can also be cause by a dirty
sensor! Think about it, the 02 sensor sits in the dirty exhaust manifold all day long sucking up heat, fumes, fuel, emissions, and dirt and never has a bath !!!

Good Luck

Tim
all day