I want to know when a running process will terminate. How can I watch it?

Run this:

while kill -0 <PID>; do sleep 1; done; echo "Process finished at $(date +"%F %T")."

Or you can make a bash script. wait-for-death.sh:

#!/bin/bash

if ! kill -0 $1; then
    echo "Process $1 doesn't exist."
    exit 1
fi

while kill -0 $1; do
    sleep 1
done

echo "Process $1 finished at $(date +"%F %T")."

Then give it execution permission:

chmod +x wait-for-death.sh

and run it passing the process' PID:

./wait-for-death.sh <PID>

If you want to avoid PID collisions you can use at:

job_id=$(at now <<< 'sleep 10' 2>&1 | awk 'END {print $2}')
while at -l | grep -q "^${job_id}\s"
do
    sleep 1
done
echo "Process finished at $(date)"