That makes it tough to inspect the fixed cup as well as you can when you remove it, IMO.

I always remove it, clamping blocks of wood on either side of the BB to hold the fixed cup wrench on the fixed cup and then hitting the end of the fixed cup wrench has never failed me, and generally they spin right out without all that much of a fight anyway. Cleaning up the threads with a wire brush followed by some fresh grease makes me happy!

I use a flashlight and my finger.

But not like ET.

I use lock ring pliers for those. I just used one recently and it came off wiithout issue. I have a few different snap ring pliers so I used one that was fairly large. It looks like this. Put the ends into the pin holes, Push in hard and turn, should come right off.

Ideally a fixed cup tool is used to remove the fixed cup. For DIY at home, oftentimes a big ass crescent wrench is enough to remove the fixed cup on old French bikes. Or a vise. There is also a well known 'cheat' method on Sheldon Brown's page.

Pull the cranks first. Then the adjustable cup. Dump out the spindle and bearings. Then take off the fixed cup. 70s Peugeots are usually French threaded which has a right hand threaded fixed cup, but that looks like it could be an 80s bike, which can be anything. Is there any writing on the other side?

+1 on getting a proper lock ring tool. IMO it is next to impossible to adjust properly without one. A basic open (one tooth) Hozan type is fine.

That is true, generally speaking. However, in this case the frame is going to be powdercoated.

Didn't the OP's pic show 1.37. That's English threads, not french or swiss, correct?

Proper, thorough and correct service will always include removing, cleaning, inspecting the fixed cup, bearings, threads and interface.

Proper bottom bracket service means installing on a shell that has been correctly chased and faced, using a bottom bracket tool, not a wrench.
https://www.hozan.co.jp/cycle_e/catalog/BB/C-358.html

This is also the proper tool for removal.

A bottom bracket that has been properly installed as above should not have its fixed cup removed for regular servicing (repacking). BITD people didn't have 5 bikes. Racers and enthusiast cyclists rode 300+/week. BB bearings got repacked about twice a year on average, more if caught in the rain. Fixed cups were not removed until the bottom bracket was worn out and replaced. It would have been silly.

An old bike of unknown history that's been sitting for decades generally should have both cups removed for servicing.

Agree to disagree.

"back in the day", that was then, this is now.

Most of the bikes we deal with are of unknown history.

Nothing silly about being thorough but sidestepping is asking for trouble that won't be silly.

As always you are welcome to do it your way but not to pass judgement on my methods or rationale, that's just silly.

With the cup removed you can lay a nice symmetrical bead of grease around the cup for the bearings to sit in, with the cup in the frame your ability to get a decent uniform bead of grease in the cup is notably reduced, so removing the cup likely saves time, and if you had it out 6 months ago it'll spin right out "now".

As a kid I did a lot of maintenance on a fleet of 30 rental mountain bikes (Chrome Mongoose ATBs), I always removed the fixed cup when servicing them, my boss was an old road racer, thats how he wanted it done, worked great for me then, and now.

I fully agree that a BB can be regreased with the cup in the frame, I just don't think its the best way to do the job.

I removed my BB so I can get my frame and fork powder coated. It went very well, the lock ring and adjustable cup came off easily and the fixed cup wasn’t really very tight either. The bearings are caged and all the parts look nice. There was plenty of grease on everything. Thanks for all your help!
oh, you’re right, the Park Tool spanner is junk!

Good on ya for tackling the job, won't always go well and that's when some practice will really help. The fixed cup should be good and tight when you put it back together.
Again, knowing how it goes when it goes well will really help when it doesn't. The lockring spanner always takes some finesse but some work much better than others, I swear by the Sugino, the hook end and the fixed cup end both work very well for me and I would encourage you to find one that works good for you.