Sean Mandell -- creator of the "Spilling Royal Tea" podcast -- shared his insights on "TMZ Live" shortly after Kate's health revelation Friday ... saying the silver lining in the devastating news may lie in the small window of opportunity for the two to finally patch things up.

Mandell reminds us Harry actually used to be quite close with Kate -- in fact, he practically third-wheeled loads of her public engagements with William ... this before Meghan Markle came along, which created an undeniable divide between the trio.

However, SM tells us that something of this magnitude has the potential to melt any icy feelings between Harry and William -- and he suspects there may be a reconciliation.

As we reported ... Harry and Meg sent their well-wishes to Kate Friday, not long after she revealed she was battling cancer. Unclear if any future visits across the pond are planned.

While Mandell believes Harry will reach out to Kate personally -- which may lead to some fence-mending between him and his sibling -- it's hard to tell if the 'Fab 4' will get back together the way they used to be pre-Megxit ... there's been a lot of bad blood since.

In any case ... Sean says the Royals will pull together one way or another -- especially on the issue of Royal duties. Lots of other Royals are stepping in, and he thinks even Harry might get back into the mix now that both his father and sister-in-law have fallen ill.