Some sleuthing reveals that, yes, layout has a custom setindex! https://github.com/jkrumbiegel/GridLayoutBase.jl/blob/6734d2ad247361261b343975fe36a7c6604de8fb/src/gridlayout.jl#L1033
It took a bit of searching with JuliaHub to find this out, but in general, the way you could do it simply at the repl is using the @which, or @less/@edit macros. E.g.
julia> @which a[1] = 2
setindex!(A::Array{T,N} where N, x, i1::Int64) where T in Base at array.jl:766