Please,,,,before you start doing anything under the dash,,disconnect the battery. It only takes a touch of a small wrench across a hotwire to ruin your day,,and make more under dash problems for you.
Being the "reasonably capable tinkerer" that you are,youll hafta pull the speedo and get into it from there. Take it apart and see if it just dont need a small drop of light lubricant........
you can hook it up to a cordless drill to check your progress.Or find a good used one in the "parts wanted" column, or on evil bay.
Good Luck,
Marty