The 法句經 (T210) has a parallel verse (at T210.4.563a8) that reads:
獨行遠逝，
覆藏無形，
損意近道，
魔繫乃解。
Traveling alone, going far away,
Hidden away without form,
The controlled mind approaches the way
And is freed from Mara’s bonds.
To answer your question 獨行 = ekacara, which literally means “going alone” or “solitary travel.”
The 出曜經 (T212) also has a parallel verse (at T212.4.774a24), too:
遠逝獨遊，
隱藏無形，
難降能降，
是謂梵志。
Going far away travelling alone,
Hidden away without form,
Controlling what’s hard to control,
One is called a Brahmin.
Here, the C. trans. is 獨遊 for ekacara, which has the same basic meaning, but 遊 has more of a sense of wandering or “going for a walk” without a particular destination.
The commentary that follows says that the mind is said to “travel alone” because it only abides in a single kind of sensory object at any given time. But it moves freely from one thing to another like a bird flying or a king who travels with servants who have every provision that he might need. This was answering a question about the mind possessing the ten mahābhūmika dharmas, which was an early Sarvastivada Abhidharma model of mind. The servants in the King metaphor represent these mahābhūmikas. (There’s a list of them at this Wikipedia page on mental factors.)
SuttaCentral says 法集要頌經 (T213) has a parallel at Chapter 31, verse 8 (if I’m understanding the numbers used correctly), but I don’t see anything close to the Dhammapada verse in that chapter. However, the parallel listed in Chapter 33 (at T213.4.799a27), is nearly verbatim the verse in the 出曜經. The translator is using five-syllable lines instead of four, so he’s inserted a fifth character into the lines, but the changes (bolded below) are superficial.
遠逝獨遊行，
隱藏無形影，
難降能自調，
是名為梵志。
In the third line, 自調 means “to tame oneself,” so the line would translate to “Taming what’s hard to control oneself.” The other additions are superficial.
There’s also evidence of a Gandhari version in John Brough’s The Gandhari Dharmapada (p.139), but it’s only a fragment of part of the first line:
duragama eka …
Hope that helps!