Apologies for the wall of text, but I want to check to see if I am interpreting this correctly - magical activities will leave a signature on whatever it is used on and said signature can then be tracked (if it is noticed in the first place) at increasing threshold until it finally disappears. Which leaves magicians who do not clean up after themselves magically vulnerable for quite a few hours after using their mojo?

I can see the worse case scenario already: Mr Bad-ass Wage Mage (with a brace of bound, high level spirits) is called in to investigate the site of a break in on Corp X's property. The magically active intruder happened to leave a signature behind which he is able to assense.

Calling in his posse of spirits, he then gives them the following orders: follow the astral link of this signature to its source, then manifest and teach an object leason to the shadowrunning scum about why they should not mess with corp X. The posse of spirits should not take more than a couple of hours (using teamwork) to follow the link.....and half a dozen or so spirits manifesting unexpectedly on top of any PC mage should cause a world of hurt.

Have I missed something or should magicians be real careful about what traces they leave behind? (especially the ever popular overcast stun spells ... thats a long time for the signature to disappear)

That's the whole reason why there are metamagic techniques like cleansing and flexible signature in the first place.

So yes. Be carefull about your magical fingerprints.

Would you guys be so kind as to tell me if I have the mechanics right?

Astral Tracker arrives on the scene shortly after a Force 5 spell is cast. His threshold on the astral tracking test is 5, so he rolls and gets, say, 2 hits. Since it has been an hour, the threshold is increased to 6. He rolls again and gets, say, 2 more hits. Now it's been 2 hours, and he has 4 hits accumulated, but needs to get 7 now. He rolls again and gets 3 hits, so he finally tracks the original spellcaster down after 3 hours. If he hadn't reached the threshold by his fifth test, the tracking attempt fails because the signature he was following has evaporated.

Is that right?

Yeah. But remember he first has to assense the signature if the spell itself is over.

Important to note! Yeah, if he doesn't get (3 + hours past casting) hits on the assensing test, he can't start tracking. Thanks, now I know what to do when I run a game.

This actually came up in a game I ran last night. I'm clear enough on astral signatures left by magicians, but what about a spirit? You can trace the link between a spirit and a magician, but the elemental isn't leaving the magician's signature at the crime scene, it's leaving its own. Does this then mean that you'd have to trace the signature back to the spirit and then trace the link from the spirit to the summoner? If that's the case, is the tracker simply out of luck if the spirit has returned to the metaplanes on standby?

Do spirits keep memory of their previous summonings? If so, maybe the spirit could just be questioned.

I think that is up to the game. I try to run it as all spirits are NPCs, even magician summoned ones, though my players haven't really interacted with them much.

It's kinda fun because a single mage could potentially have 5 dozen or so different NPCs that can all have different personalities, etc. I also like to think about what they might be up to on their metaplane when they aren't under the PC's instruction.

To assense the signature itself he has to get 3 hits + mods by MBC or Flexible Signature. Yet to start the tracking the hours past are counted on the TH.

Just to make it clear Astral Signature =/= Astral Link
An Astral Singature is kind of a magical Fingerprint. Nothing more nothing less. So if you don't have a reference it is worthless.
An Astral Link is an astrally visible connection between a magician and his spells, foci or spirits.

The weird thing though is that Astral Links seem to persist indefinitely, using them to track someone just takes longer and longer. No matter how old the link is, as long as the searcher gets 2 or more hits on every test, the link can be tracked.

There is no mechanism for summoning a specific spirit nor does the book state whether spirits continue to exist after the services are fulfilled, so tracking a magician via his spirits is a gray area rules-wise.

OK, so you CAN'T track someone based on seeing an astral signature! That makes them far less worrisome (or useful, depending on your outlook).

So, from the standpoint of a mage-detective, an astral signature is only useful for identifying the person or thing that made it if you somehow happened across them again. There is no tracking down a mage who just mindraped someone in a club unless the perpetrator left a focus there or something.

I think it follows that there's no summoning up a specific spirit that used to belong to someone you want to track, because once you do, that spirit has a new master and is no longer an astral link to the old one.

EDIT: But the threshold modifier listed in the OP seems to indicate that you CAN track something based on the signature! If you had an active link, the threshold would not increase, but stay at 5. Inactive links, i.e. signatures, get harder and harder to follow as time goes by.