For the first time, I noticed that Paul Atkinson is using a bit of vibrato.
More significantly, I realized that there's a similarity between "This Old Heart of Mine" and "Whenever You're Ready" in that - unless I'm mistaken - the guitar parts in both feature pairs of notes an octave apart.
According to the Zombie Heaven booklet, "Whenever You're Ready" pre-dates "This Old Heart of Mine." A demo was recorded "April or June 1965," and the released version was recorded on 24 June 1965. According to the chronology in the booklet, this television appearance (on Dents De Lait Dents De Loups) was on either 29 or 30 October 1966, and the liner notes of The BBC Radio Sessions add that the Zombies recorded further live versions of "This Old Heart of Mine" on 1 November 1966 and 10 October 1967.
The liner notes of both Zombie Heaven and The BBC Radio Sessions seem to indicate that the Zombies used the Isley Brothers' version of the song as a basis for their cover. I hadn't heard it before, but I found it on YouTube (here's a link to the official lyric video). It doesn't have these octave pairs (not on guitar, at least), so it seems that this is something that the Zombies added to the song, re-using an element from "Whenever You're Ready."