How do you change the value a timer sends on the Time Expired Ping in Rec Room?

The Timer Expired pin from a timer will always output a 1, so to change it you need additional logic built around the Timer Chip.

Use a comparator as a gate that checks for when the timer expired pin fires (i.e. is not 0). When that happens, the value through the cyan pin (depicted as blue in this image) will be passed through to the red output pin. In all other cases the value through the magenta pin (depicted as cyan in this image) will be passed through to the green output pin.

With this logic you can have a baseline value that is present when the timer has not expired and then a different value pulsed when the timer does expire. You can remove the plus chip and then just use the red output if your baseline value is just 0.