[FOM] Avoiding patterns/RCA/WKL

[pax0 at seznam.cz]

It is well-known that there is an infinite word not containing a square (avoiding the pattern xx)
over the three letter alphabet {0,1,2}.
My question is: Do we need WKL over RCA for this result?
The intuition is that there is a finitely branching tree of square-free prefixes in which we have to find an infinite branch.
But is WKL really used here?
Thank you, Jan Pax