Okay, I have a character who is perpetually packing a semi-automatic handgun in a shoulder holster, so that the gun is under his arm.
This is going to sound like a stupid question, but does this only work if he's wearing some kind of jacket?
No, it works fine with other dress apparel as well.
Like, if he's only wearing a t-shirt, the holster would go on top and then the gun would be visible. But could he wear a sweater over that? Or would it still be obvious?
Depends on what your wearing and packing. You could be giving off a profile for the smallest ACP if you had it in a speedo, or nothing at all even if your packing a desert eagle under a parka. It'll vary.
Just try to make your cover appropiate to the locale. Up north, the yankies are used to wearing heavy clothes so it'll be easier to pack. Down south, it may be odd if your wearing a windbreaker.......but if your wearing a sports jersey like some of the hoodrats do, it'll be harder to spot a weapon signature.
Whatever you wear, practice, practice, practice with it in that style of garb.
Sometimes you won't give a rats tail if your profiling. Sometimes it'll be to your advantage to let them know your packing for action. Macho or not, that's life. They might be less inclined to jack you.
Also, what are the basics of cleaning a handgun? Does one oil it?
Unless your planning on writing for the NRA, the average writer won't care.
Sweaters are fine, up north. Again, whether your profiling the signature or shape of the weapon will depend on what type it is and how you carry it.
A smaller or medium frame weapon will have a lower overall shape/profile than a large frame will. A kidney holster or small of back will also be easier to hide if you wear loose baggy clothes. Coats are fine as long as they appropriate for the locale.
They make these new tshirts that have built in holsters that you can wear under a loose over-shirt. Designed for the drug-units down in Dade County/Florida. Those might work for you. They have 'em in small/medium and large frame. They all have sewn in magazine holders. The guy who makes does a special order job for the drug-guys that one sewn in holster under each arm with 4 or more magazines along the lower back. Nice, but they don't work under body armor. Go figure. Reasonably priced at 30-60 bucks U.S..