When inside Palatine Hill or The Forum, is it possible to pass back and forth between them without needing an additional ticket?
Yes! They are connected inside the security perimeter so you can travel on foot between them. There is a map of sorts on this page of the Coopculture website; click "load the map":
https://www.coopculture.it/en/poi/roman-forum-and-palatine/
This can be a useful site for some background reading:
https://parcocolosseo.it/en/visit/opening-times-and-tickets/24h-colosseo-foro-romano-palatino/
(Edited to add)
I'm crossing fingers that Rick's map that accompanies his free, downloadable audio tour of the forum is still accurate; it indicates where the internal crossover between Forum and Palatine is located.
http://podcasts.ricksteves.com/pdfs/forum.pdf
Thanks for the detailed information. I was hoping that someone who has been there recently could confirm the "crossover" is still there.
They've always been considered a single attraction, meaning they don't sell tickets for them individually. I would assume they'd only eliminate the crossover if they decided to do that.