I realized that there are some similarities between this and the keyboard solo (Hohner Pianet + Vox Continental) in the alternate take of "Nothing's Changed" (track 15 on disc 3 of Zombie Heaven), which is something like this:
Both consist primarily of a repeated set of descending triplets (although the intervals in the two parts aren't the same), and both start with an eighth note pick up and an ascending fourth.
According to the Zombie Heaven liner notes (p. 52), the Zombies performed "The Tracks of My Tears" live, so it's possible that the melody and rhythm of the vocal part here had something to do with Rod Argent's keyboard solo in "Nothing's Changed," even if merely subconsciously.