Use the control mode (`tmux -C`) and parse the output.
Quick and dirty script, a proof of concept:
#!/bin/bash
pane="$1"
trap 'SECONDS=0; dte="$(date)"' USR1
unset TMUX
kill -s USR1 "$$"
tmux -C attach | while read -r a p z; do
[ "$p" = "$pane" ] && kill -s USR1 "$$"
done &
while sleep 1; do printf '\r%-12d %s ' "$SECONDS" "$dte"; done
Usage: `./scriptname %N` where `%N` is the ID of the pane you want to monitor (e.g. `%0`; usually you can get it with `echo "$TMUX_PANE"`). Monitoring the pane where the script runs is possible but makes little sense.
Tested with `tail -f /var/log/syslog` in the monitored pane and `logger` elsewhere.