Hello Adrian:
There is only one vaccination that has an associated legal requirement (by international treaty), and that is Yellow Fever.
Travellers need to show proof of Yellow Fever vaccination when arriving from countries where Yellow Fever is endemic or has been recently reported present.
A few third-world countries require travellers arriving from anywhere to show proof of Yellow Fever vaccination. I don't know if any of your planned Central and South American destinations are among those who require travellers from anywhere to show proof of vaccination.
For more information, see this World Health Organization document: Yellow Fever Country List.
Be aware that this past summer, the WHO announced that Yellow Fever vaccinations will now be valid for the lifetime of the person who has been vaccinated. Previously, a vaccination was required once every 10 years. See this press release for more details: New yellow fever vaccination requirements for travellers.
Michael
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