As a touareg owner buying a VCDS cable and downloading the software would pay for itself on the first occasion it saved you a trip to the dealer. And there will be many such occasions on this sophisticated vehicle. Beware ebay copies. Buy direct frim Ross-Tech.com and get it right the first time.
Yes, this is precisely the sort of adjustment you can make to your vehicle. It is called coding. My T1 has 27 control modules, read mini-computers, and many must be coded. This enables VW to produce vehicles which can be adjusted to each country's laws, etc. Your T3 will have the more sophisticated Long Coding on some modules. VCDS walks you through those with the Long Coding Helper.
As I mentioned, on my T1 there are two codings given for the trailer module. These are the simpler 7-digit codes. If your T3 uses this coding system it should be coded to 0000002 for North America. At least one poster thought your trailer light issue might be ROW (rest of world) coding, 0000001.
Of course, you will probably use VCDS much more often to view and erase the fault codes stored by these myriad control modules. Many of them are intermittent or flaky but will nevertheless shut down a system until erased.