It is in the very first sentence you quote my friend. Emphasis is mine.
A pilot may not continue an approach below the Category I decision height ... unless at least one of the following visual references for the intended runway is distinctly visible and identifiable to the pilot
If you only see and can correctly identify one item from the list, you are permitted to continue the approach. That's it, that's all. Nice and simple, no more lawyering required. Well, that is until it's not. What comes next is an understanding of how the lighting systems work, because without that you can't practically follow the rule. While truckflyer may have been quoting FAA rules, the design and use of approach lighting systems are international in nature.
Each element of an approach lighting system is designed for you to see and identify at a certain point in the approach. For consistency sake, when you will see each element is based on distance from the runway, not time. If you are approaching in a 172 it will take you far longer to cover the same distance as a 737. For example, what the FAA terms an ALSF-I, ICAO terms a CAT I Lighting System. It's all the same, just with different names. You learn about their setup during training for the instrument rating. There are at least 16 different approach lighting systems as defined by the FAA, even more if you include the non-standard systems. ICAO simplifies the list to something like four or five, but all that does is class those 16 systems into different groups. I've come to find I prefer knowing exactly what system I'll be seeing as there is too much variation otherwise. Most, but not all, approach charts will show you what lighting system is in use. If it's not on the approach chart, it'll likely be on the airport chart.
You asked about a CAT 1 approach, so let's look at that, and using a CAT I/ALSF-1 lighting system. I'm going to use feet in my explanation, whereas you'll read about them in meters if you're asking about CAA/EASA. When you hit minimums, you'll first see the sequenced flashers (colloquially known in my neck of the woods as "the rabbits") and centreline bars anywhere from 2,400 to 3,000' from the end of the runway. This is what permits you to continue the approach below minimums and, knowing that you need 1/2sm visibility or 2600 RVR, you'd see the runway or runway threshold lights almost immediately thereafter. But, we're talking approach lighting right now. You'd continue your stabilized descent until you could identify the 1,000' bar, so called because it is a three-part bar of white lights located 1,000' from the end of the runway. Immediately following this you'd see the side row bars (coloured red) with the centreline bars continuing until you see the 500' bar - again, so called because it is 500' from the runway, and includes a full row of white lights between the side row bars. 500' later you would see the runway threshold lights.
That's the sequence for ALSF-I. In an MALSF system you'd have most of the same lighting as ALSF-I, except there are no side row bars and no 500' bar. Or there is SSALR where the sequenced flashers are only installed for about the first 1/3 of the distance, where you'll then see two centreline bars at 1,500' and 2,000' from the runway, followed by a 1,000' bar which itself is followed by centreline bars spaced every 200'. I hope you can see from this why it's better to know what lighting system is in use, rather than knowing it's simply 'Category I' as there is so much variation in that statement.
As for going around after 2 to 3 seconds, you're not leaving yourself a lot of time to identify the next element in the system. Approaching at 85 knots (a light single such as a 172 or PA28), you need something like 17 to 21 seconds from minimums until landing. Doing that in a 737 or A320 approaching at 140 knots, you need 10 to 13 seconds. After 2-3 seconds you're not giving yourself enough of a chance to even see the 1,000' lights, never mind the runway.