Its the 172SP I did difference training on. I'll take your word its only 13, definitely a lot more that the AT3 which has just 1. Main problem is keeping track of which you've done as several are grouped together.
If you're going to be flying a particular airplane / variant of an airplane, when considering preflight checks start trying to establish a routine. Means get someone to give you their checklist and explain / demonstrate what needs to be checked for each point on that list. Then check each individual point in turn according to the list. With experience you might consider writing your own lists in order to create a flow list but for the time being, just stick to following the list, mentally checking off the individual points.
With regards fuel drain points, for the 172R / 172S there are 5 under each wing so I tend to work from a given point - my routine is to start inboard front, then go to on the next one - inboard rear - from there move back to the front of the wing and a bit further outwards - and do each one in turn. The same goes for the three under the engine - here I work from the front backwards. If you stick to your routine, after a while you'll soon know which have been checked because your position under the wing will tell you which ones have already been checked.......