I've never taken a 102's keyboard apart, nor have I seen the "insides"
like you describe them, but that little thing in the rubber cap you
mention as a "metal stud"...likely isn't metal.
Based on keypads and other similar kinds of "button devices" I've taken
apart (remote controls, calculators, etc) - it's actually some kind of
plastic or rubber compound impregnated with carbon. It does actually
complete the circuit, as you stated.
But I've also found when I've tried to bridge such a circuit with just a
piece of metal...getting it to work can be "finicky" - assuming in your
case it works at all, and the break isn't somewhere else.
Cleaning of the contacts as suggested is a good step, though I don't
know if you need to necessarily use an eraser; they tend to be abrasive,
which in the case of cleaning contacts you'd think would be okay, but
realize that the metal layer of those contacts is very thin. One such
"cleaning" won't harm it, but do it enough times...hopefully that won't
be needed or necessary, of course.
You might try just using the alcohol (and a swab), first (I have a
"thing" when cleaning things, especially if solvents and plastics are to
be involved: start with the least harmful first, then move up the chain
- that's usually either soap and water, or rubbing alcohol; end of the
chain, of course, is a right angle grinder and/or "blue wrench" and/or BFH).
Regardless, try also some rubbing alcohol on that little stud, as it can
sometimes get dirt and/or other deposits that can prevent the circuit
from being made.
Good luck!
Andrew L. Ayers
Glendale, Arizona
phoenixgarage.org
github.com/andrew-ayers