How can I merge a Modified Date and Time in Twig?
Having done some further testing and research I believe this is a case of having to merge two date objects and ensuring that these are set as date/time objects when merging them into a variable.
Here are some examples way:

{% set thisWeeksDayAndTime = thisWeeksDay|date() ~ ' ' ~ classStartTime|time() %}

{% set thisWeeksDay = page.startDate|date_modify('this  ' ~ classDay ~ ' ' ~  classStartTime|time()) %}