The necklace in the advertisement is not, in my opinion, the one we have seen photographed on the Countess.
Closer view of item in the ad.
The Countess wearing her necklace
It is possible that the Countess was selling jewellery at this time (May 1960) as her husband had died on 13 January 1960; yet the estate hadn't been submitted for probate then.
During the 1960s there were other sales by the Earl of Pembroke and the Dowager Countess.
The Earl, 1961
The Dowager Countess 1968
The Dowager Countess 1969