QUOTE (shinyjam @ Aug 20 2012, 11:25 PM)

From memory, the spell signature last for Force X Hour.
Erasing an astral signature (SR4a p. 179, require astral perception) just need a number of complex action equal to the force, which is basically like 30 seconds to wipe away a force 10 spell. So there's no reason not to always wipe your spell signature.
Yes you were in a fight which went for 2-3 combat turns... you left how many astral signatures.
Your GM is not going to give you minutes of free time to clean up your signatures?!
Very nice GM... with HTR and/or the star on the way. Or the security spider is bringing building security online and you need to rush things along.
Sorry this argument is one completely situation dependent on the GM being lax with the players and allowing tons of times between encounters. You better not cast any spells to cover your retreat because you'll have no time to scrub either! Unless you have invested in metamagics it's going to take a substantial amount of time in SR turns to clean things up. All I take this to mean is the GM is not adequately pressing the players.
On to the last bit:
The search power... "The being may seek any person, place, or object. To find the target, the creature makes a... test. The critter must have seen what it is searching for before; spirits may search out anything that their summoner provides them with a mental image of."
At the very least they have your magical 'fingerprint'. It can be used to ID you and your team later or in a court of law.
So yes the focus can most definitely be searched for provided the spirit or mage has seen it's aura before (highly likely if he's the one who put it there, even if he unbound the focus after it was stolen so it couldnt' be used as a ritual link against him).
Some GM's consider magical constructs like spell signatures astral objects. And also allow them to be searched out... in this case... they might search for wards with your fingerprints or search for other copies of your spell signature to find other places you've been.