If there's still 12V on the coil with the key out, likely to be the ignition switch inside the column gone loopy.
That was my first thought, the fuel cut off solenoid is specifically to prevent this from happening. Easy enough to test too
If Its not the shutoff solenoid issue where hot spots of glowing carbon are enough to ignite the mixture (not really dieselling more glow plug engine) .. There is a strange one where if you dont have lots of electrical toys drawing current from the ignition circuit the current through the dashboard ignition warning light is just enough to power the coil. Aftermarket alternators with smarter regulators have a different behaviour on the D+ line.. it's either hard on at 12 volts(lamp off) because the regulator is happy, or its grounded because of a fault / problem or startup mode (lamp on) . No dim glowing. This could make the problem worse than before you changed the alternator. The good thing with these regulators is you only need a low current LED as a warning light and they should still work properly. And that LED would stop the alternator back feeding the ignition.. Or you fit electronic ignition that will tend to shut off when fed less than 6 volts.
Wow didn't understand a word of that I think it will have to go to the man! somebody did mention a little squirt of WD 40 down the barrel?
If you have a later bay with the multi plug on the ignition switch Then you can pull off the multi plug and plug in a new ignition switch and use a flat bladed screwdriver to start it. This will allow you to see if your current switch is knackered without too much fuss Edited to add if you decide to take it for a drive make sure the key is in the ignition and the steering lock is off.
Tldr : changing to an aftermarket alternator could be the cause of your problem. If you can, post a video of what happens,, there could be clues. And sometimes trying to read some more about the problem may avoid you having your pockets emptied by somebody who turns out to have little more idea about electrics than you, but is good with a spanner.
WD40 is a water dispersant. When you spray it on caked up grease or oil it dissolves the grease or oil . But by itself it can actually make things more sticky as it doesnt contain any oil. There was a test done a few years back where it was shown to improve the adhesion of shoes on a fibreglass surface (deck shoes on a yacht deck) for instance. Buy a can of contact cleaner for electrical contacts (but the ignition switch on a bus is a rather sealed crimped together thing that no spray will reach, if the switch is worn out, replace it) Use graphite lubricant for locks. Use spray grease for greasing things, or 3 in 1 oil for lubricating them.