No need to guess about what is in and what is not in GPX. Refer to the GPX standard:
GPX 1.1 Schema Documentation
The GPX file format is only at version 1.1. That's because it was developed in 2002, and the last modification was in 2004. The main problem is that GPX is a
de facto standard, and even worse, a standard created by a single company. There's no standards body meeting regularly to decide on improvements, as there is for, say, HTML.
To see any improvements in GPX, we would need one of these companies to take the initiative and get the interested parties together.
That having been said, GPX 1.1 is sufficient for the application mentioned (stopping over). No changes to the standard are required. You simply list the waypoint/point twice, with two different times. The fact that you haven't moved between those two time points indicates that you've stopped over.