Raspberry PI with Monitor.

The cheapest way to create a timer system is the use of a raspberry PI and monitor (and keyboard/mouse).

Only extra needed is a long HDMI cable from Raspberry PI to the monitor. Since controlling the timer is on a different location than showing the display in the archery range.

Extension to multiple displays.

There is a simple way to extend to multiple displays by adding a video splitter. (and extra cables).

For more info about Raspberry PI for ArcheryClock, see Link.