Just did a quick test on the LS demo site and seems like it is not timestamps that are saved per question, but rather the timing in between.
18,"2019-09-17 01:11:57","2","en","1658867261","2019-09-17 01:11:47","2019-09-17 01:11:57","
demo.limesurvey.org/index.php?r=admin/su....26","","6.91","4.35
"
However, you have the timestamp when the survey was started and you have the last time stamp as well, so you probably could calculate the timestamp per question group based on this.
Or you could write the timestamp into a hidden question (not via GUI, but CSS). I am not sure how this could be done, though. Not an expert on JS.