The Thirds and Fourths Tenor evolved from the older Invader Style Tenor (developed in the 1940’s) which had the F#4 located in the middle of the pan. Pan tuning techniques evolved to include the tuning of an octave partial on the note panels around 1965. On the Spider Web lead (the ancestor of the 4ths and 5ths pan), the physical proximity of the octave notes in relation to the octave partials meant that those pans had a brighter, louder sound because the octave partials caused the adjacent octave note-panels to vibrate sympathetically.
Bands using the Invader style lead found that they could not compete sonorically with bands using the 4ths and 5ths layout, because the octaves on the Invader Style were placed across the pan from each other, and so did not add any acoustic support.
As a result, some bands in Trinidad (Carib Tokyo, Amoco Renegades) went about trying to address the design issues inherent in the Invader Style pan, and came up with the Thirds and Fourths layout. This layout was still the predominant lead pan layout in Renegades when I played with them in 1994.
Most of the rim notes on this layout are positioned in the same/similar positions as they appear on the Invader Style pan, with the exception of F#4 which has been moved from the center of the pan to the rim. The higher octaves of all notes have been moved to be adjacent to their lower counterparts in order to make induce sympathetic resonance.
On some versions of this layout the F#4 and Bb4 are switched.