1993 Lexus GS300. 187K miles and I'm pretty sure the oxygen sensors have never been replaced. Online sources indicate they are a wear item and should be replaced every 60K to 90K miles. Car is running very rich periodically. No trouble codes thrown as far as I know (CEL is off). No other issues with the car.
They're definitely wear items, and that old, they're not the heated/wideband kind (almost certainly the single wire sort). I like to replace them every 80k miles or so, though when I was running a fleet of used vehicles of substantial age/mileage, I just replaced them when I got the car and did the general tuneup (plugs, wires, cap, rotor, oxygen sensor, filters, etc).
I think if it was the case that a O2 sensor was bad, sometime in the past it might have create a diagnostic trouble code that may or may not have made the malfunction indicator light come on. so checking for trouble codes at auto zone or buying your own Bluetooth ELM327 dongle will tell you this.
If an oxygen sensor fails, it will usually throw some variety of code on just about anything, to include pre-OBDII vehicles. The problem is that they rarely fail, and only fail entirely at extreme miles. The typical failure for a single wire sensor, especially, is that they get lazy and slow to switch. The narrowband type (a 93 is almost certainly using a narrowband) doesn't really tell you how rich or lean you are, just that you are. So, the engine computer enrichens the mixture until the sensor says rich, leans it out until it says lean, and just oscillates back and forth at cruise. Sometimes this will get fed into a learning system that can compensate for a partially plugged injector or something when in open loop mode, but as the sensors get lazy, the crossings aren't as accurate, so you typically see a slow loss in fuel economy as the computer just isn't getting as rapid of data. They're not "failed" - just no longer working as hoped. But the computer can only detect a failed condition. As long as they're switching, the older ones won't throw a code.
Newer, heated, wideband sensors (typically a 4 wire harness) give you more accurate information about the actual fuel/air mixture, and come up to temperature far more quickly (helps with cold start emissions). I don't know as much about how they fail, not having owned many of those.
on an old car like this there is the possibility of end of life failure issues coming up on almost every part of the car, so it could be costly start swapping out parts. For myself, in the past, once I spend some money then the sunk cost fallacy kicks in and will lead to even more spending to make the already spent money 'less' wasted.
I generally disagree, having owned an awful lot of old vehicles that other people considered "end of life." One I literally pulled from the junkyard, one I rescued from the junkyard in the "Junkyard offered $X, beat it and the car's yours" phone call variety. Plus others that were hardly low miles. I've run one vehicle to end of life (or, rather, various other people did - I tended to loan that one out for cheap), and when it went to the junkyard, it was done. Just about everything that could fail was either failed or failing, and it didn't have a lot of systems to start with. But outside serious rust (which can't be the case if a 93 is still rolling around), the only way you get a bunch of system failures is if you don't maintain the vehicle properly (in most cases). Sure, you might need to put a new transmission in at some point (get a junkyard one from a wrecked vehicle, it'll probably be fine), and given enough miles on a high strung engine, you might want a junkyard motor, but I generally disagree with the "It's old, therefore maintaining it is pointless" approach to vehicle ownership I see depressingly often.
Also, if you're doing the work yourself, the cost is minimal. If you have friends who you can trade labor (and maybe some garage space) with, it's even better. I know this isn't a thing anymore in most areas, but... man was it nice. If you have a group of friends who all work on older/cheap vehicles, cost to keep one running is quite low.
If I just replace the TPS or pay someone to replace the TPS, is that something that would likely fix this kind of issue? Or is it more likely that a wire is loose or flakey somewhere and that problem needs to be addressed?
Go poke around the wiring harness for a while. Oddball failures are rare. If the whole harness is creaking and shedding insulation, you probably have a wiring issue. Otherwise, the far more likely case is that the TPS is going bad. They're usually variable resistors and they do wear out.
I'm inclined to think that the TPS itself is probably fine, and that it is a loose / bad / old / wire that is failing. I'm also inclined to think that if I go to someone and say, "trouble code 41" that their inclination will be to replace the TPS rather than do what I would imagine to be fiddly work of checking wires and connections and voltages and stuff. I'm also inclined to think that I'm not sure I could find a good mechanic who is willing to do the fiddly work rather than just replace-and-hope.
Why would you think the TPS is fine with that kind of miles? Have you just replaced it?
If it were my car, I'd do the same thing a mechanic would. Replace the TPS and clear the codes. If you still have issues with a presumed-good TPS (I'd say known-good, but I've put bad parts on a car, new out of box, and so have most of my friends - quite the irritating issue), then hunt wiring, but unless you've got some very, very good reason to check the wiring, it's probably the TPS.
Do you have an old mechanical multimeter? You can probably test it easily enough and see if it's smooth and within spec. I'd use a digital one to see if it's within spec, and a mechanical one to make sure it moves smoothly, but... just replace it.
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Bigger problem I see here is that you have a 27 year old vehicle and don't appear to be fully comfortable working on it yourself. That
will eat you alive. You seriously need to be able to work on a car that old yourself, because nobody else is going to want to and will charge you the "Ugh, I don't want to do this..." rates.