one way to narrow down the possibility would be to add some sort of tank decoration just a little ways from a wall. try to use something that would be "comfortable" for a fish -- a relatively smooth peice of driftwood or plastic, or a plant with big stiff leaves like an amazon sword. put in the tank so that your BGK can in essence "wedge" himself behind it and rest while remaining relatively upright. a gap of two to three times his width should do it.
i suggest this because in my LFS, i always see the knifefish behind the driftwood and whatnot, leaning against them. i would think that if your BGK was on his side because he was tired, then he would welcome the addition of a place to lean against (given the preference of most fish to remain upright).