Alright Adder, I promised I'd look things over and here's what I've got.

1. Patrol IC automatically examines all "loud" icons every turn. If you are a loud icon and do not have a mark on the host, then you are unauthorized and it triggers the alert. (I don't know if this is a valid scenario- is there a way to enter a host without having at least one mark?)
This sounds right, but I don't think there's any way for a person to enter a host without a mark. At least, not yet. It's possible we'll see some stuff with the deep dives that have been hinted at.
2. Patrol IC will scan for silent icons "periodically". That depends on host configuration, security level, "alert status" of the host. For example, if another hacker just broke into the system and was caught, Patrol IC would constantly scan for silent icons which might catch me even though I haven't done anything yet.
This is what I envision the Patrol IC's primary job is going to be. I agree that this all depends on the security level and alert status of the host. Generally, I wouldn't do more than one scan per turn just to prevent bogging things down in the Matrix. Also, I would assume that any icon that the Patrol IC has already scanned is on the "okay" list and won't be re-scanned unless something changes. Such as a security elevation, or one of the triggering events mentioned below.
Here's how I see the Patrol IC working, step-by-step:
- Hacker enters host using Brute Force
- Patrol IC immediately elevates the security level by 1 (corresponding security protocols are followed)
- Patrol IC begins scanning for silent icons
- If the Patrol IC finds a silent icon, it raises the security level by 1 again (corresponding security protocols are followed)
- Hacker enters host using Hack on the Fly
- Patrol IC scans the new icon in the host (if running "loud")
- Patrol IC scans for silent icons
- Patrol IC finds a silent icon, it raises the security level by 1 (corresponding security protocols are followed)
Once the Patrol IC has scanned your icon, you are clear to travel about the host (assuming you have a mark and aren't skulking about).
3. If the Patrol IC spots a silent running icon, it will check if they have a mark. If they have a mark they will ignore them, but they're still spotted so an illegal action would automatically be detected. (You could change this so that any silent running icons are always illegal and immediately trigger an alert but that feels a little harsh).
It does feel harsh, but that's one of the side effects of breaking into a corporate host. If you get caught sneaking around, security-minded folks will automatically assume you're up to no good. And a host is much like a corp's private turf - they have full extraterritoriality and they will use it. Note that a Patrol IC may not make an alert known system-wide, rather just sending a subtle message to the decker on duty.
4. Whenever an illegal action is committed, the Patrol IC does a Matrix Perception test to detect the aggressor. Spotting will result in an alert. Even not spotting could result in increased "alert status", see #2 above, depending on the host.
In the event that the illegal action is discovered (such as using Brute Force or failing a Hack on the Fly action) then yes, I think this makes sense. The term demiGOD gets used a lot for system administrators of hosts. However, they aren't directly affiliated with GOD and therefore don't have access to quite the same protocols and tools. With that said, breaking into hosts sneakily is really the prefered method of hacking specifically because a host can lock itself down super-quick if needed.
5. Whenever some other custom-defined action is taken, the Patrol IC does a Matrix Perception test as above in #4. This is configured by the host. For example, if there's a super special file that only the owner should be able to edit, that would count as an "illegal action" and trigger #4's test. Note that a host -defined illegal action does not increase overwatch score.
Seems reasonable to me. I don't know if every host requires a specific set of events to be created. You could probably get away with just using the idea that every time the host gets a mark on something, the Patrol IC investigates what that something is.
I just realized I should probably outline what I see as a reasonable security protocol list.
Security level 1:
- Alert the decker assigned to host security
- Decker decides whether or not the threat is a false alarm
- Launch a single instance of White IC (I like Marker and Tar Baby)
Security level 2:
- Alert the decker assigned to host security
- Decker personally investigates the alert
- Launch a single instance of Blaster, Killer, or Sparky IC
- Command Patrol IC to start scanning for silent icons every turn
- Command Tar Baby IC to attack any icon revealed by the Patrol IC
Security level 3:
- Launch instances of all remaining IC available (starting with the deadly stuff and working down from there), remember the host can only launch one IC per turn
- Command Tar Baby to link-lock every icon it can find