In ACM Queue, I defined FQDN as follows:
The DNS namespace has a tree structure, where every node has a parent
except the root node, which is its own parent. Nodes have labels that
are from 1 to 63 characters long, except the root node whose label is
empty. A domain is a node in context, and a fully qualified domain
name has a presentation form that is just the node names, bottom up,
with each followed by a period (.). For example, www.google.com is the
fully qualified name of a node whose name is www, whose parent is
google, whose grandparent is com, and whose great-grandparent is the
Any time you use terms like "host name" or "host part" or "domain part" you are off in the weeds and you'll find that no definition of FQDN quite fits your purpose. The meaning, rather than the definition, of FQDN can be made clear by considering its antonym: the non-fully qualified domain name. To be fully qualified means you're specifying all domain labels up to the top level, and you could in that case append a final dot (.) to indicate that you've done so. To be less than fully qualified means that the name you're looking at only makes sense within the context of a search-list or default-domain.
RFC 1535 was interesting because a lot of us had up until that time used multi-label local names and still expected search-list behaviour -- and this broke too many other things, so was outlawed. But when I was firstname.lastname@example.org in 1988-1993, it was possible to send mail from email@example.com to matt@decvax and have it expanded to firstname.lastname@example.org and email@example.com and it all just worked. Turned out we had to give that up. These days if there's a dot in your presentation-level name (that is, you typed it or a program displayed it), it's presumed by all the software in the world to be an FQDN.
My Sendmail book (co-authored with Fred Avolio after we'd both left DEC.COM) also has a chapter on this topic, which is interesting reading since it was written at the same time as RFC 1535.