Okay, realized I had a pdf of Chainmail available, now this is interesting…
First of all, it does indeed give a duration for Ghoul paralysis, even if it's only given in game mechanic time.
What I have is listed as Chainmail 3rd edition, so I don't know for sure if it's what OD&D was defaulting to when the little brown books were published, but here's what it says about Wights and Ghouls:
If they touch a normal figure during melee, it becomes paralyzed and remains so for one complete turn. A paralyzed figure is considered to be able to strike a blow at the Wight just prior to paralysis taking effect, so melee can occur but only one round.
As it's the 3rd edition of Chainmail, I'm glad to see they at least started spelling "paralyzed" correctly (leading me to think this edition was printed after the first D&D pamphlets). So far I haven't determined how long a "complete turn" is in this game. I haven't read it cover-to-cover (and won't be doing so), but I have not found it defined in any real-world terms, nor is it stated whether the terms "turn" and "round" in this book are synonymous. As roleplaying wasn't a part of Chainmail, I suppose having a real-world equivalent of those terms just wasn't necessary.
Anyway, here's the part that really interested me, Wraiths also had a paralysis ability, but without a duration, rather, a simple cure:
WRAITHS (Nazgul, etc.): …paralyze any enemy man — excluding all mentioned in the fantasy supplement **— they touch during the course of a move (not flying). Paralyzed troops remain unmoving until touched by a friendly Elf, Hero-type, or Wizard.
** I take it by this they mean Heroes, Super-Heroes, Wizards, Elves, Dwarves, Hobbits, and the humanoid races, so apparently the paralysis power of Wraiths was limited to what became known as 0-level humans, and is dispelled by the touch of an Elf or any human above 0-level.
So, as Chainmail was often recommended to use in D&D, and the Fantasy Supplement section officially called by Gygax the source of the D&D, or some similar phrase, one can reasonably look back to it for interpretive guidance, and also understand that paralysis inflicted by undead was not likely meant to be unending until some method of reversal was researched by players.
I think it's likely the absence of duration in OD&D, Holmes, and 1st Ed AD&D is due to the authors being so familiar with the rule that they either never thought to write it down, or kept thinking they already had.