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Unfortunately it's not an obvious gap in paint or sealant, as it looks likely that the rot pre-dates the current decoration.
Which is not surprising considering the other things going on in this place.
I'll be following @bq's suggestion & filling it with epoxy for the moment.
Eventually, I'll need to replace it, as I'm repairing the stone sill & building up a runoff on it*, meaning that the wood needs to be replaced anyway.
* It's pooling water at the moment - no doubt adding to the existing problems caused by any leaky surrounds.
More damp woes - While making the sandstone windowsill a little less shit, it turns out that the wooden sill of the sash window is rotten.
What's a quick & dirty fix that will stop it getting worse and prevent damage to other parts of the wood frame?
Eventually, I'll get someone in to repair it properly, but it's way down the list at the moment.