What was found
A/P PITCH TRIM CAUTION LIGHT CAME ON WHILE CLIMBING THROUGH 10-12 THOUSAND FEET. UPON DISENGAGING THE AUTO PILOT, ACFT PITCHED UP SLIGHTLY DUE TO NOSE UP PITCH SETTING, PITCH TRIM ADJUSTED BACK DOWN WITH THE NORMAL TRIM SWITCH AND CAUTION LIGHT WENT OUT. UPON RE-ENGAGING THE AUTOPILOT THE CAUTION LIGHT CAME BACK ON AND NOSE PITCHED UP WITH A RUN-AWAY PITCH UP CONDITION. DISCONNECTED PITCH TRIM WITH EMERGENCY DISCONNECT SWITCH, & LANDED UNEVENTFULLY. REMOVED HORIZONTAL STABILIZER TRIM ACTUATOR AND INSTALLED REPAIRED UNIT IAW CMP 274301. PERFORMED HORIZ. STAB TRIM SYSTEM FUNC. TEST IAW MM 27-40-00. PERFORMED AUTOPILOT FLIGHT DIRECTOR FUNC. TEST IAW G200 CMP 224010.