Swapping boards is a good way to determine problems. Swapping ICs would be next to see if any are bad.
Removing the trigger light is easy. It snaps in. Pry the black cap of the back. You can ohm out the lamp to see if it is open before removing the cap. If the lamp is bad, it is a 683.
The knobs on the time base have a narrow range of position when put back on. If the large knob is put on too far back, it will do what you are seeing. There will be too little back movement. Move the knob out a bit to see if that helps. Cleaning the switches will help. You may have to remove the board to get access to the set screws on the part that moves the switches if moving the knob does not help. Make sure not to allow the cams to turn if you remove the board! Be sure not to loose the pin that pushes the nylon bobbin that actuates the microswitch lever. The clear part that shows the time/div. adjusts the amount of movement. That also has a narrow range it can be secured to open and close the switch.
The Var. control can come out by loosening the set screws on the collar that is connected to the black part to the control. You do not need to remove the readout board to do this step.
You may have to have both shafts out to get them straight.