No sensor I can think of showed a climb. None.
What was the most telling thing was that just a few hours after the incident Bill Clinton went on TV to proclaim that no DoD sensor data was available. BS. Anyone who has ever been in that field knows what sensor data was available for that flight and there was plenty of it.
There were several military radars that showed the entire event, including one that showed two blips, possibly three, of a mach 2 object coming toward and intersecting the TWA-800 aircraft. These military radar would show not only distance and direction, but also altitude, not relying on transponder returns for that data. ALL of these military radar recordings were immediately sent to the White House and were never seen again.