Are you sure it's the switch? My father and I have both had problems with the overdrive button on our 4+3 cars and one thing was a constant, the wires to the switch had fatigued and eventually so many strands were broken at the solder joint that the button no longer worked. His repair was limited to just soldering the wire back on the switch's posts, however when I fixed the lead on my 86, the overdrive still would not engage. I initially thought I had a bad switch, but it tested good across the ground pin,which is the center contact, and the pin with "NO" (Normally Open) stamped above it. With an Ohm meter on the ground and "NO" pins you should momentarilly read continuity across the switch when you push the button. If the switch tests good, it is most likely the overdrive relay located on the firewall next to the brake booster that is the cause, as it was on my car. Other possible causes are low ATF fluid in the overdrive, a bad low pressure switch in the overdrive. The relay was a cheap fix at $18 and for good measure I ordered a new 4+3 filter and gasket so that I was certain the fluid was clean and full. For $55 the tranny was back to normal, it left my wondering what a dealer would have charged me to fix it. $500 ? $1500 ? or "you need a new transmission". I hope it's a simple problem like mine was. If you do find that it's the switch, search this forum under "4+3" or "Doug Nash 4+3" and you will find a thread on the part which is still available from the O.E.M supplier to GM.
Good Luck