Yeah, looking less and less like something I can fix myself.

Same brand/type bulbs and switch (but not fixture) are used in both bedrooms with only one having the issue.

I've already checked that the lugs are tight but I didn't pull on any wires, I'll double check that those wires are secure.

Dim, various levels, vary rapidly for about a second. Also at varying intensity, one time might be barely noticeable and the next you'd think the power was about to shut off.

I've not noticed anything other than the one light.

Panel pics - Oven is bottom right breaker, light is on the one directly above it (again, nothing else on this circuit seems affected).

Well I checked and didn't find anything loose either on the oven or light circuit. Another item that may or may not mean anything - the breakers are right next to each other. But then again the light circuit includes stuff like my PC/Monitor and the other bedroom's light none of which have issues.

Might just have to suck it up and pay a pro.

I will check that. Not sure if it matters (regarding the power co. side of things) but ground and neutral are on the same bar in the box, house was built in the early'40s.

As far as I remember it was happening before I switched to LED bulbs.

Sounds like it could be that the ballast was going bad. Plug and play LED replacements still need a good ballast to work and will not work by bypassing, you need the direct wire type for that.

So your options are to replace the ballast and keep the plug and play LEDs or get new LEDs designed for ballast bypass.

Well that's not confusing at all, lol.

Here's my guess: the 4 conductor wire (black/white/red/ground) is coming from the breaker box (with everything disconnected the red/black wires would be hot with the breaker on) and the 3 conductor wire (black/white/ground) feeds the rest of the circuit.

You'd want to use the red wire (hot) to the brass screw and a pigtailed* white wire (neutral) connected to the other white wires to the silver screw. Pigtail* a ground wire with the other ones and put it on the green screw. The black (hot) wires don't need to be touched.

I would also wrap those ground wires up with electrical tape and/or cover the connections on the back of the new part because with those connections being open and the ground wires not being shielded there's a good chance of creating a short as you shove everything together when you're done.

*explanation video here

Edit: Didn't think about it being a switched outlet like the other post says. Haven't had to deal with those so feel free to ignore all but the last part about eliminating the possibility of a short.