Charles Davis's database basically confirms this: for the 1881-2 series (in which the first and last Tests were drawn) it says the matches were "Advertised as timeless but effectively limited to four days". Apparently the England team toured New Zealand between the first two Tests. Presumably the itineraries in later series had more leeway.All Tests in Australia were timeless until WW2. There were a couple of draws when the visitors had a boat to catch.
The timeless Tests in SA were in 1923 and 1939 (the infamous 10-day Test); the SA v Eng series in 1927-8 and 1930-1 evidently didn't end with a timeless Test even though neither series was decided by then. The WI one was in 1930.
I had the impression that the final Test in 1930 was made timeless because the series at that point was *level* rather than just undecided - I thought I'd read that if England had hung on for a draw in the 1930 Lord's Test, they'd have drawn the Oval Test (which didn't end until the 5th day, partly because of wet weather) and won the series. (I can't remember where I read this, and haven't managed to confirm or refute this claim since).