For sure the masterplayers of III-COLOR-CHESS in future need a 3-Chess-clock. There are variable kinds of clocks for 2-Chess. A 2-Chess-clock always shows the looser of the game. It is the one, who has overstepped his agreed time limit.
But for III-COLOR-CHESS we need a clock, that shows the winner (remember the Highlander-rule)! And such a clock works in the contrary way to a normal Chess-clock. Of course the 3-Chess-clock has three time segments (LCD-displays) steered by a microprocessor, and some keys to set time and switch to the next player. The segment of the player on move is inactive, while the other two segments are running. So both the other players collect the time the player on move loses. The first one, who has collected an agreed time is the winner. A III-COLOR-game takes one and a half as long as the agreed time limit maximum.
Nowadays it is modern to give time bonus per move. This Fisher-mode is thinkable for the III-COLOR-CHESS-clock, but I haven't made it. Our endgame knowledge doesn't justify this investment yet.