This works in both directions, right?
It is clear that an observer can notice the lingering astral signature and that it can be compared with the magician if they ever meet later.
It is clear that an observer can notice the astral signature of the magician and that it can be compared with the the lingering astral signature at a later point.
It also clear that an observer can use astral tracking from the lingering astral signature at both where the spell was cast and at the target of the spell to track down the magician responsible for it.
What you are asking is if you can use astral tracking on the magician to find any and all sources of magic he left in the world. The answer to this is no.
If someone assenses the spellcaster, is it immediately obvious that they're sustaining a spell, considering that the enspelled object is elsewhere?
If an observer assenses the spellcaster it is not even immediately obvious (= that you don't even require a test to notice it) that the subject is awakened in the first place (this require that you both actually take the time to observe the living aura of the subject as well as that you you get at least one net hit on the reading test).
One thing that would be immediately obvious (= not even require a test to notice) is if the subject currently have an active spell attached to its aura (as the active spell would have a tangible astral form that is immediately obvious). But to find out if the spell originates from the subject or if it was left there by someone else you need to either compare their respective astral signatures (manage to read an astral signature require that you take the time to observe both the astral form of the spell as well as the living aura and that you get several net hits on the reading tests) or astral tracking (observe the astral form, successfully read the astral signature of the spell and then successfully use astral tracking to find its source).
If someone assenses the briefcase, can they tell that there's a sustained spell on an object inside it?
No, while physical object might appear as intangible shadows of their former self for an astral observer, they are still 100% opaque and 100% block astral perception from sensing whatever is inside (or behind them).
A dual natured entity (such as a magician using astral perception) would need to first physically open the briefcase.
A wholly astral entity (such as a magician using astral projection) could potentially specifically push his awareness inside the briefcase without issues (unless there is some sort of magic ward or other astral form protecting it).
Also, note that if the briefcase is carried though an astral form (such as a ward) then the astral form (for example the ward in this place) and the spell sustained on the pebble inside the briefcase will cause an astral intersection (which will disrupt the spell sustained on the pebble, the astral form it was pushed through - or, on a tie, both).
Is the link only visible at the endpoints, or can it be discovered somewhere in between?
The link can be picked up at two locations.
1. The location where the spell was cast (if you drive by casting a spell then this location will be inside the van - if you cast the spell while in an ally you will leave a lingering signature in the ally)
2. The target destination location of the spell (if you cast it on a pebble then it will linger on the pebble - if you cast an AoE spell in an office then you will leave a lingering signature in the office).
There is no link in-between. And there is no link to be picked up at the source itself (the magician that cast the spell).
Is the link a straight line
Book doesn't tell. But considering using astral tracking to find the source is a time consuming endeavor that at the minimum take one hour to complete (and where partial success does not seem to bring you closer to your target than a total failure) I would say that it is more complicated than following a straight line from the lingering signature back to whatever was responsible for it.