Yes, I noticed that 'your' TR4 has a later radiator -- the one with the crank hole was used on the early 4s.
It's something to think about. That original radiator was replaced for a reason so possibly it needs work -- but at least the owner did the decent thing and saved the original part.
Some delete the hole on TR3 & early 4s to increase/improve cooling. I kept the hole on my TR3A and have no cooling issues driving in one of the hottest climates in the US -- but I suppose if I had been fighting overheating I would have been tempted to delete it when I got the radiator re-cored. As it is, I enjoy the novelty of crank-starts and the handiness of the crank when adjusting valves and setting timing.
In addition to the crank hole that spare radiator probably has a long neck to the cap -- this was leftover from when that same radiator was used for the TR3 which required that filler neck to clear the rear edge of the apron. Once those TR3 radiators were used up TR4s got their own design which is what yours appears to have now.
Sure looks like a good car beneath a dubious paint job, look forward to hearing about your plans for it. Not every car must or should be a show car -- solid drivers are a lot of fun and getting harder to find.