[link to original on tumblr]
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I think there might be some connection between this and "Soulville," which the Zombies performed on the BBC. In both bridges, one phrase of the melody is almost entirely one note. In "Just out of Reach," it's "Time will show that I mean what I say, you'll see," and in "Soulville," it's "I'm gonna see all the folks and know all the tricks, oh yeah." (Little Richard's "Long Tall Sally" is an-other song with a mostly one-note phrase: "Gonna tell Aunt Mary about Uncle John / He claims he has the misery, but he has a lot of fun, oh, baby," and - as I've mentioned before - I think the Beatles' "I'm Down" and Argent's "He's a Dynamo" have this feature too.)
According to the Zombie Heaven liner notes, the Zombies performed "Soulville" on 26 January 1965 (for eventual broadcast on 6 February), and I'm assuming that it was in their repertoire for awhile before that. There's at least a full month between that BBC performance of "Soulville" and recording "Just out of Reach" (2 March 1965), so it's possible that Colin Blunstone took some inspiration from that, but - again - it's just a conjectured influence.