Simple way to check the game board signal..... that I use anyways.
Remove ALL color inputs to the monitor. Red, Green, and Blue.
(leave the sync hooked up as it is)
Use just one input wire, in this case we'll use the red one since it's your question color, and connect it to ANY of the color inputs on the monitor.
If anything shows up using that red wire from the game board, then the signal is working from the game board.
Doesn't matter what "game screen" it on. Game mode, test mode, whatever.
If you get something only when you connect the red wire to either the green or blue input....and nothing on the red input...... then it's a problem with the tube or chassis.
You kinda have to ignore what color you see while doing this, all you want to note is if the red signal from the game board is working.