LEAR 55 PITCHED DOWN AFTER AUTOPILOT WAS ENGAGED AT CRUISE ALT; RESULTING IN AN ALT DEVIATION.

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I WAS L SEAT ON EMPTY LEG AFTER PAX DROP OFF AT LAS. I AM USUALLY R SEAT AND PNF; BUT THIS WAS MY SIC RECURRENCY FLT WITH CHK AIRMAN; WHO IS ALSO A SENIOR CAPT. I HAND FLEW THE AIRPLANE BEAUTIFULLY FROM TKOF AT LAS TO FL220. AT SOME POINT WHILE CRUISING AT FL220; CHK AIRMAN ASKED ME TO ENGAGE AUTOPLT. I BELIEVE THAT IT WAS HE WHO ACTUALLY HIT THE ENGAGE BUTTON. HE TOLD ME TO SELECT HDG MODE; WHICH I DID. THIS IS OLD STYLE INSTRUMENTATION ('STEAM GAUGES') -- THE ONLY INDICATION OF MODE SELECTED IS ON AUTOPLT PANEL ON GLARE SHIELD. SOMETIMES IN BRIGHT LIGHT; THE MODE BUTTON LIGHTS ARE HARD TO SEE. IMMEDIATELY AFTER SELECTING HDG MODE; THE AIRPLANE PITCHED DOWN SIGNIFICANTLY. I ATTEMPTED MANUALLY TO RAISE THE NOSE; BUT NO RESPONSE. WE WERE LOSING ALT. I CALLED TWICE FOR CHK AIRMAN TO DISENGAGE AUTOPLT. HE DID NOT. I THEN DISENGAGED USING THE YOKE MOUNTED DISCONNECT. DURING THIS SEQUENCE; WE LOST ABOUT 400-500 FT OF ALT. I THEN CLBED (HAND-FLEW) BACK UP TO FL220 IN A MATTER OF SECONDS. I DID NOT SEE ANY OTHER MODE LIGHT ILLUMINATED -- ONLY ENGAGE AND HDG; DURING THIS EPISODE. WE LATER RE-ENGAGED THE AUTOPLT AND IT WORKED ADEQUATELY; ALTHOUGH IT DID SEEM TO RE-TRIM MORE THAN NORMAL TO HOLD ALT; SOMETIMES DEVIATING MORE THAN 150 FT; WHILE IT WAS ENGAGED. THERE WAS NO TFC CONFLICT. IN FACT; AS SOON AS WE RE-ARRIVED AT FL220; WE WERE INSTRUCTED TO DSND TO 16000 FT. (MINS BEFORE ENGAGING THE AUTOPLT; WE DID GET A MASTER WARNING WHICH WE RE-SET AND WHICH THE CAPT/CHK AIRMAN SAID WAS MACH TRIM RELATED. AFTER RESET; WE DID NOT GET THE WARNING AGAIN.)