It seems that following someone in astral in next to impossible. Even people that are not trying to ditch you are probably moving at fast enough speeds that when they hang a corner or two you'd lose sight of them quickly. And if that person knows that you're following and they want to ditch you they'd just fly at 6000km/hr, zig-zag through a few buildings a ditch you.
Any ideas for following people in astral?

Are you claiming that you don't want to use the astral tracking rules on SR4A P. 192? That's an Assensing + Intuition (5, 1 hour) Extended test.

Or are you more interested in the immediate shadowing type of test where you do a kind of astral chase?

Astral Movement has two modes.

100 Meters a turn Walking Rate
5 KM per combat turn Running Rate

For a target "Running" I'd use the astral tracking extended test.

For a target "Walking" I'd do a Shadowing test.

Say you're astrally projecting and you come across a mage doing something shady. He takes off at "running" speed. How do you follow this guy? In a meat bod chase the person running after the other would be able to visually follow the other guy unless a corner was cut and then it's probably a perception check. Following a running astral entity seems impossible because they can zig-zag through walls while moving at 5 km/turn.

Astral Tracking isn't exactly the chase situation that I was hoping for. Besides, I don't think it would work without a link of some kind.

So basically, it appears that there is no way to follow "running" astral entities...

SR4A p. 193

"Nearly all magical things (spirits, spells, foci, and magical lodges) have
an astral link to something. Active spells are linked to their casters,
spirits are linked to their masters, astrally projecting magicians are
linked to their physical bodies, and foci and magical lodges are linked
to the magicians who activated them. Awakened entities who are aware
of these links can follow them and track them through the astral plane
back to their sources."

So in the scenario where an astral projecting mage is observed, and then leaves at "Fast" speed, since a link was there, that link could be observed and then tracked with a Astral tracking test.

Also SR4A p. 192 Astral Tracking modifiers Tables has "Each hour passed since astral link was active" as a modifier.

You can't "instantly" follow, but you can certainly have a chance to astral track.

Hmmm... not the answer I was wanting but you nailed it. Thanks Dire!