What was found
BOTH LEFT AND RIGHT BLEED AIR LIGHTS ILLUMINATED FOLLOWED BY SMOKE AND FUMES IN THE COCKPIT/CABIN. APPROX 15 MINUTES AFTER TAKEOFF, DURING FINAL LEVEL OFF AT FL 280, BOTH LT & RT BLEED AIR LIGHTS ILLUMINATED SIMULTANEOUSLY INDICATING A TAIL CONE OVERHEAT CONDITION. ACCOMPLISHED CHECKLIST AND LIGHTS WENT OUT WITH LEFT BLEED IN EMERGENCY AND RIGHT BLEED ON. LIGHTS ILLUMINATED AGAIN WHEN POWER WAS ADVANCED. SMOKE ENTERED COCKPIT AFTER 15 MINUTES OF BEGINNING EMERGENCY CHECKLIST. ACCOMPLISHED UNEVENTFUL OVERWEIGHT LANDING. INSPECTED TAIL CONE BLEED OVERHEAT DETECTION AND CHECKED FOR BLEED AIR LEAK. RAN ENGINE AND APU AT MCR. ALL SYSTEMS CHECKED GOOD.