Lua, 103 91 bytes

s,l=...s:gsub('.',load'c=...b=b or not s:find(c..c,1,1)and s:find(c,1,1)')print(b%l-1,b//l) 

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Ungolfed version:

s,l=... --Take in haystack and line width as args s:gsub('.',function (d) --For each character in s b=b or not s:find(c..c,1,1)and s:find(c,1,1) --If there is only one instance of c, store location end) print(b%l-1,b//l) --Print results