First of all, your TIMESTAMP value is never changed. A better way is to use a function to get the timestamp each time you display it.
getTimestamp() {
echo `date '+%Y%m%d-%H:%M'`
}
echo "Waiting for pids: $pid1 ===> $(getTimestamp)" >> $MYLOG 2>&1
But the problem is that the lines are written into the log file at the same time (when all the proc are terminated), so the timestamp is the same. You probably need to do it without "wait", with a loop and check the process state for each pid.