OBD-II Codes on a Mazda 626

I know this is a Miata group, but I can't find a good group to post
this question and it's probably generic to any Mazda anyway, so
forgive me in advance.

Check Engine Light came on and I got three codes

P0133 - O2 Sensor
P1131 - O2 Sensor says running too lean
P1132 - O2 Sensor says running too rich

I cleared the codes, and within minutes of driving 2 of the codes came
back.

Everything I read online said, if you're getting all these codes,
replace the O2 sensor. The only sensor I could find was the one
upstream of the catalytic converter facing the radiator. I cleared
the codes and removed the O2 sensor. I figured, "If I don't have the
correct sensor, the codes will come right back. If I've got the
correct sensor, I'll get a code to the effect that the O2 sensor is
not responding at all." Well, I drove about 30 miles and never got a
code. I figured that was good news (I had the right sensor since I
didn't get the same codes). So I replaced the O2 sensor. Within
about 10 miles of driving, I got the P0133 code again!

Is it really likely that I've got a bad sensor? The wiring looked OK
when I replaced the sensor (had to splice the new sensor to my
existing plug). I'm suspicious that the sensor is OK and something
else is going on.

Thanks in advance for any advice,
Scott