OK here is what I come up with....
AllData does not list that code at all (we already established that).
When I go to Mitchell, the code is not listed under the DTC Index when you click the link on the right side of the page. However, if I put P1627 into the "Search" in the center section, I come up with the same information that you provided.
So, apparently, Isuzu has not released diagnostic and/or repair information for this particular code to the aftermarket....it is a "Manufacturer-Specific" code, so this does not surprise me....
However, I was able to go one step further:
I am a sponsor member of iATN and have the resources available from professional automotive technicians around the world.....When I checked their "known Fixes" database, I found several listings for this same code, with the same symptoms you are describing....Cooling fans that will not shut off and a fuel level gauge and light that is extremely erratic.
Although there was about 20 listings for this same issue, I only read through three of them before coming to this conclusion:
In all three of the listings that I read (I picked them at random), replacing the fuel level sending unit fixed the problem. So it would be safe at this point to assume that code P1627 IS for the fuel level sender circuits. Makes sense to me now....an ANALOG sensor signal that must be converted to DIGITAL in order to share among different modules.
So at this point, I can only refer you back to my original post where I stated:
"The correct "fix" for this is to repair all of the sensor circuits and/or the sensors themselves so that the circuits are functioning as designed. This is the ONLY way to make the computer happy."
Repair the fuel level sensor circuits.
Let me know if I can do anything else for you.