I have pondered the activity of rummynose tetra myself. I like this fish, and I have had the "Brilliant" Rummynose (species is Hemigrammus bleheri; the original rummy, Hemigrammus rhodostomus is never seen now) continually for many years. I've also had the false rummynose, Petitella georgiae, for a few years now; this one is less intense colour, rarer to find, and grows a tad larger. I only have a few, so they are in with their cousins and the two species remain in a relatively tight shoal as they swim through the tank. They are more active swimmers than say the Rosy Tetra, cardinal, glowlight, etc, but having said that they remain in the lower third of the water (generally), and swim as a shoal, which is a lovely sight. In my view though this needs a 4-foot tank minimum, in smaller (shorter) tanks they seem "at odds" in a sense.
The swimming back and forth is normal for this species; I have seen them do this in very large tanks, and I have observed videos of them in their habitat waters behaving exactly the same. It is the most tightly shoaling characin, but it does need the length (4-feet minimum) to really show off its beauty.
Given your incredibly planted 4-foot tank, and the water level preference of the rummys and Pearls, I would not advise against the rummys if you like them. Make sure you get at least 12, but this is minimum and it would be better to go with 15 up to 20 here. I had 21 in my 5-foot tank initially, having lost a few to old age now some 7-8 years later, but they were lovely all along. I recently acquired a couple groups of new fish to keep the shoal around 15, as I have them in my 70g now. I've had this species in with sedate fish like hatchets, Bolivian Ram, and other more quiet characins, and there has never been an issue.
Byron.
). Hey, whatever gets him more interested, right? Ha ha! Maybe he's thinking this will make me more interested in football - not a chance!! 
