Move 58 and the subsequent moves should have told you that you were in a draw position. A rook file pawn king ending should always end in a draw unless your opponent blunders. Obviously, after move 62 he wasn't going to. But to answer you question, when you think you have the advantage always go for the win untill it's obvious it's a draw.
Taking the draw, or going for the win
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I just finished a live game that ended in a draw. My opponent asked for a draw when I was better (Stockfish says I was around +0.45), and then again in an a-pawn + king vs king-ending. I did not take the draw the first time with equal material and a better initiative (I felt). And since we are both low rated players I did not take the draw in the ending; how could I know if he knew what he was doing or not? Then he called me a dickhead for wasting his time (in a three minute game he invited me to play ...) What do you think? Should I have assumed that he knew how to play the ending and taken the draw, or is it OK to play on in a drawn position to see if you opponent can hold the draw?