-out of the wall to the outside?
-ceramic, integral with the ceramic of the sink feeding into the waste pipe?
-or a separate pipe from the overflow hole that links in just below the plug hole?
As its from 1959, I'm guessing the first. Im a little confused as to your problem as for you to be concerned about your overflow being blocked, I'm presuming your sink must also be blocked? or you are constantly filling your sink too much anyway for it to become blocked or for you to be concerned about it getting near that level.
The solution depends on the type of overflow, for example on a modern sink I would disconnect the overflow pipe from the waste (after the sink is empty!) and just flush it through outside before reconnecting. For a porcelain overflow you could try a 'drain unblocking chemical' although these are nasty and shouldnt really be used very often (or arguably at all) especially with plastic pipes. You could try a pipe cleaner or a rod. If the overflow leads straight out side, you could try just rodding it through to the outside and/or try it from the outside inwards.
he only solution I have come across is to use a small bore flexible pipe connected to the hot tap and used to "jetwash" the debris out. You can't use a rod as there are too many sharp corners. The blockage is most likely to be where the passage in the porcelain joins the plug hole. Once there is a passage open, use a drain cleaner to open more.
This will at best only be a partial cure because the only way to clear all the debris is to remove the waste (plughole), but that may be awkward and difficult and will require replacing as you will not be able to use the old seals.
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