Random, wild electrical issues?

Update: 144,083 miles.

I purchased this car for $500.00 from my uncle. Because it had sat idle for over a year, I replaced everything: hoses, battery, tires, alternator, fuses, brakes, spark plugs, shocks, etc.

And then it started acting weird electrically.

Sometimes the radio will come on and the key isn’t in the ignition.
There’s a light burning smell.
Sometimes the interior lights work and sometimes they don’t (no rhyme or pattern, just random).
Dashboard lights flicker on and off.
Radio turns on and off on its own.

Every place I’ve taken it to (two dealerships) they’ve said it will take about $500.00 just to see what the problem is, not even to fix what’s wrong which could be thousands of dollars they’ve said.

What I keep hoping for us to find someone who can walk me step-by-step through what to do with this car to get to the bottom of what’s going on. The car is a classic and I’d like to salvage it if I can and if I can’t, I’d like to know definitively from someone who knows what they’re talking about that it’s a loss.

I have a really solid guy who can look at anything someone asks us to check, he’s just not an electrical guy and doesn’t even know where to begin.