I find that the overthinking can be fun, but the most common cheating method is to simply relay the position on the board that contains the piece to move.
For example, let's say that the best move would be to move a pawn on b4 (same column as White's left most bishop, in the 4th row) a signal would be transmitted of two short "signals", a long pause, and then four more short "signals". Thinking in Morse, this would be "../....".
This tells the cheater that the correct move is made by the piece in the second column, fourth row, and thats usually all a top level player will need. They can stop calculating any move that isn't from that piece, and there's usually one move that is clearly better from that pieces immediate moves. The difficult part is now finding which follow-up moves are the best and how to punish your opponent for not playing them (which they would have been doing anyways, just with many more possible start points)
This method has been used in the past with a device that will send a non-painful but noticeable electric shock to a player (usually on their thigh), and because these individuals got caught there are now methods in place at top level tournaments to try and prevent external cheating devices from entering the playing hall (ex/ they pat you down to try and feel something rigid on your leg).
Thats where the butt plug theory comes in; it could theoretically pass through a standard metal detector, a security guard isn't going to check your prostate for cheating devices, and it can still theoretically be used to communicate via 0s and 1s.